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Journal articles on the topic 'Pseudo-Riemannian manifolds'

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Published: 4 June 2021

Last updated: 29 January 2023

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1

MANTICA, CARLO ALBERTO, and YOUNG JIN SUH. "PSEUDO-Q-SYMMETRIC RIEMANNIAN MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 05 (April 3, 2013): 1350013. http://dx.doi.org/10.1142/s0219887813500138.

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In this paper, we introduce a new kind of tensor whose trace is the well-known Z tensor defined by the present authors. This is named Q tensor: the displayed properties of such tensor are investigated. A new kind of Riemannian manifold that embraces both pseudo-symmetric manifolds ( PS )n and pseudo-concircular symmetric manifolds [Formula: see text] is defined. This is named pseudo-Q-symmetric and denoted with ( PQS )n. Various properties of such an n-dimensional manifold are studied: the case in which the associated covector takes the concircular form is of particular importance resulting in a pseudo-symmetric manifold in the sense of Deszcz [On pseudo-symmetric spaces, Bull. Soc. Math. Belgian Ser. A44 (1992) 1–34]. It turns out that in this case the Ricci tensor is Weyl compatible, a concept enlarging the classical Derdzinski–Shen theorem about Codazzi tensors. Moreover, it is shown that a conformally flat ( PQS )n manifold admits a proper concircular vector and the local form of the metric tensor is given. The last section is devoted to the study of ( PQS )n space-time manifolds; in particular we take into consideration perfect fluid space-times and provide a state equation. The consequences of the Weyl compatibility on the electric and magnetic part of the Weyl tensor are pointed out. Finally a ( PQS )n scalar field space-time is considered, and interesting properties are pointed out.

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2

Blažić, Novica, Neda Bokan, and Zoran Rakić. "Osserman pseudo-Riemannian manifolds of signature (2,2)." Journal of the Australian Mathematical Society 71, no. 3 (December 2001): 367–96. http://dx.doi.org/10.1017/s1446788700003001.

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AbstractA pseudo-Riemannian manifold is said to be timelike (spacelike) Osserman if the Jordan form of the Jacobi operator Kx is independent of the particular unit timelike (spacelike) tangent vector X. The first main result is that timelike (spacelike) Osserman manifold (M, g) of signature (2, 2) with the diagonalizable Jacobi operator is either locally rank-one symmetric or flat. In the nondiagonalizable case the characteristic polynomial of Kx has to have a triple zero, which is the other main result. An important step in the proof is based on Walker's study of pseudo-Riemannian manifolds admitting parallel totally isotropic distributions. Also some interesting additional geometric properties of Osserman type manifolds are established. For the nondiagonalizable Jacobi operators some of the examples show a nature of the Osserman condition for Riemannian manifolds different from that of pseudo-Riemannian manifolds.

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3

Suh, Young Jin, Carlo Alberto Mantica, Uday Chand De, and Prajjwal Pal. "Pseudo B-symmetric manifolds." International Journal of Geometric Methods in Modern Physics 14, no. 09 (August 2, 2017): 1750119. http://dx.doi.org/10.1142/s0219887817501195.

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In this paper, we introduce a new tensor named [Formula: see text]-tensor which generalizes the [Formula: see text]-tensor introduced by Mantica and Suh [Pseudo [Formula: see text] symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. Then, we study pseudo-[Formula: see text]-symmetric manifolds [Formula: see text] which generalize some known structures on pseudo-Riemannian manifolds. We provide several interesting results which generalize the results of Mantica and Suh [Pseudo [Formula: see text] symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. At first, we prove the existence of a [Formula: see text]. Next, we prove that a pseudo-Riemannian manifold is [Formula: see text]-semisymmetric if and only if it is Ricci-semisymmetric. After this, we obtain a sufficient condition for a [Formula: see text] to be pseudo-Ricci symmetric in the sense of Deszcz. Also, we obtain the explicit form of the Ricci tensor in a [Formula: see text] if the [Formula: see text]-tensor is of Codazzi type. Finally, we consider conformally flat pseudo-[Formula: see text]-symmetric manifolds and prove that a [Formula: see text] spacetime is a [Formula: see text]-wave under certain conditions.

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4

Klepikova, S. V., and T. P. Makhaeva. "Mathematical Modeling in the Study of the Ricci Operator on Four-Dimensional Locally Homogeneous (Pseudo)Riemannian Manifolds with Isotropic Weyl Tensor." Izvestiya of Altai State University, no. 4(114) (September 9, 2020): 92–95. http://dx.doi.org/10.14258/izvasu(2020)4-14.

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It is known that a locally homogeneous manifold can be obtained from a locally conformally homogeneous (pseudo)Riemannian manifolds by a conformal deformation if the Weyl tensor (or the Schouten-Weyl tensor in the three-dimensional case) has a nonzero squared length. Thus, the problem arises of studying (pseudo)Riemannian locally homogeneous and locally conformally homogeneous manifolds, the Weyl tensor of which has zero squared length, and itself is not equal to zero (in this case, the Weyl tensor is called isotropic). One of the important aspects in the study of such manifolds is the study of the curvature operators on them, namely, the problem of restoring a (pseudo)Riemannian manifold from a given Ricci operator. The problem of the prescribed values of the Ricci operator on 3-dimensional locally homogeneous Riemannian manifolds has been solved by O. Kowalski and S. Nikcevic. Analogous results for the one-dimensional and sectional curvature operators were obtained by D.N. Oskorbin, E.D. Rodionov, and O.P Khromova. This paper is devoted to the description of an example of studying the problem of the prescribed Ricci operator for four-dimensional locally homogeneous (pseudo) Riemannian manifolds with a nontrivial isotropy subgroup and isotropic Weyl tensor.

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5

Jana, Sanjib Kumar, Fusun Nurcan, Amit Kumar Debnath, and Joydeep Sengupta. "On Pseudo-Petrov Symmetric Riemannian Manifolds." Advances in Mathematical Physics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/9615053.

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The present paper deals with pseudo-Petrov symmetric Riemannian manifolds whose space-matter tensor satisfies a special condition. Firstly, basic results of pseudo-Petrov symmetric Riemannian manifolds are obtained. Then, pseudo-Petrov symmetric manifolds which are Einstein, quasi-Einstein, and locally decomposable are examined and some theorems involving these manifolds are proved. Finally, two examples proving the existence of pseudo-Petrov symmetric Riemannian manifolds are given.

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6

Güler, Sinem, and Sezgin Demirbağ. "Riemannian manifolds satisfying certain conditions on pseudo-projective curvature tensor." Filomat 30, no. 3 (2016): 721–31. http://dx.doi.org/10.2298/fil1603721g.

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In this paper we determine some properties of pseudo-projective curvature tensor denoted by ?P on some Riemannian manifolds, especially on generalized quasi Einstein manifolds in the sense of Chaki. Firstly, we consider a pseudo-projectively Ricci semisymmetric generalized quasi Einstein manifold. After that, we study pseudo-projective flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.

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7

Shukla, S. S., and Uma Shankar Verma. "Paracomplex Paracontact Pseudo-Riemannian Submersions." Geometry 2014 (May 7, 2014): 1–12. http://dx.doi.org/10.1155/2014/616487.

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We introduce the notion of paracomplex paracontact pseudo-Riemannian submersions from almost para-Hermitian manifolds onto almost paracontact metric manifolds. We discuss the transference of structures on total manifolds and base manifolds and provide some examples. We also obtain the integrability condition of horizontal distribution and investigate curvature properties under such submersions.

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8

Shaikh, Absos Ali, and Shyamal Kumar Hui. "ON PSEUDO CYCLIC RICCI SYMMETRIC MANIFOLDS." Asian-European Journal of Mathematics 02, no. 02 (June 2009): 227–37. http://dx.doi.org/10.1142/s1793557109000194.

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The object of the present paper is to introduce a type of non-flat Riemannian manifold called pseudo cyclic Ricci symmetric manifold and study its geometric properties. Among others it is shown that a pseudo cyclic Ricci symmetric manifold is a special type of quasi-Einstein manifold. In this paper we also study conformally flat pseudo cyclic Ricci symmetric manifolds and prove that such a manifold can be isometrically immersed in a Euclidean manifold as a hypersurface.

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9

MANTICA, CARLO ALBERTO, and YOUNG JIN SUH. "PSEUDO Z SYMMETRIC RIEMANNIAN MANIFOLDS WITH HARMONIC CURVATURE TENSORS." International Journal of Geometric Methods in Modern Physics 09, no. 01 (February 2012): 1250004. http://dx.doi.org/10.1142/s0219887812500041.

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In this paper we introduce a new notion of Z-tensor and a new kind of Riemannian manifold that generalize the concept of both pseudo Ricci symmetric manifold and pseudo projective Ricci symmetric manifold. Here the Z-tensor is a general notion of the Einstein gravitational tensor in General Relativity. Such a new class of manifolds with Z-tensor is named pseudoZ symmetric manifold and denoted by (PZS)n. Various properties of such an n-dimensional manifold are studied, especially focusing the cases with harmonic curvature tensors giving the conditions of closeness of the associated one-form. We study (PZS)n manifolds with harmonic conformal and quasi-conformal curvature tensor. We also show the closeness of the associated 1-form when the (PZS)n manifold becomes pseudo Ricci symmetric in the sense of Deszcz (see [A. Derdzinsky and C. L. Shen, Codazzi tensor fields, curvature and Pontryagin forms, Proc. London Math. Soc.47(3) (1983) 15–26; R. Deszcz, On pseudo symmetric spaces, Bull. Soc. Math. Belg. Ser. A44 (1992) 1–34]). Finally, we study some properties of (PZS)4 spacetime manifolds.

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10

Mantica, Carlo Alberto, and Young Jin Suh. "Recurrent conformal 2-forms on pseudo-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 11, no. 06 (July 2014): 1450056. http://dx.doi.org/10.1142/s021988781450056x.

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In this paper, we introduce the notion of recurrent conformal 2-forms on a pseudo-Riemannian manifold of arbitrary signature. Some theorems already proved for the same differential structure on a Riemannian manifold are proven to hold in this more general contest. Moreover other interesting results are pointed out; it is proven that if the associated covector is closed, then the Ricci tensor is Riemann compatible or equivalently, Weyl compatible: these notions were recently introduced and investigated by one of the present authors. Further some new results about the vanishing of some Weyl scalars on a pseudo-Riemannian manifold are given: it turns out that they are consequence of the generalized Derdziński–Shen theorem. Topological properties involving the vanishing of Pontryagin forms and recurrent conformal 2-forms are then stated. Finally, we study the properties of recurrent conformal 2-forms on Lorentzian manifolds (space-times). Previous theorems stated on a pseudo-Riemannian manifold of arbitrary signature are then interpreted in the light of the classification of space-times in four or in higher dimensions.

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11

Blaga, Adara M., and Antonella Nannicini. "On curvature tensors of Norden and metallic pseudo-Riemannian manifolds." Complex Manifolds 6, no. 1 (January 1, 2019): 150–59. http://dx.doi.org/10.1515/coma-2019-0008.

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AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n.

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12

Velimirović, Ljubica, Pradip Majhi, and Uday Chand De. "Almost pseudo-Q-symmetric semi-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 07 (May 24, 2018): 1850117. http://dx.doi.org/10.1142/s0219887818501177.

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The object of the present paper is to study almost pseudo-[Formula: see text]-symmetric manifolds [Formula: see text]. Some geometric properties have been studied which recover some known results of pseudo [Formula: see text]-symmetric manifolds. We obtain a necessary and sufficient condition for the [Formula: see text]-curvature tensor to be recurrent in [Formula: see text]. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric [Formula: see text] is an Einstein manifold under certain condition. Moreover we deal with [Formula: see text]-flat perfect fluid, dust fluid and radiation era perfect fluid spacetimes respectively. As a consequence, we obtain some important results. Finally, we consider [Formula: see text]-spacetimes.

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13

Gulbahar, Mehmet. "Qualar curvatures of pseudo Riemannian manifolds and pseudo Riemannian submanifolds." AIMS Mathematics 6, no. 2 (2021): 1366–76. http://dx.doi.org/10.3934/math.2021085.

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14

Fels, M. E., and A. G. Renner. "Non-reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension Four." Canadian Journal of Mathematics 58, no. 2 (April 1, 2006): 282–311. http://dx.doi.org/10.4153/cjm-2006-012-1.

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AbstractA method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2, 2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is simply connected, then it is shown to be diffeomorphic to ℝ4. All metrics for the simply connected non-reductive Einstein spaces are given explicitly. There are no non-reductive pseudo-Riemannian homogeneous spaces of dimension two and none of dimension three with connected isotropy subgroup.

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15

Gadea, Pedro M., and Jos� A. Oubi�a. "Reductive homogeneous pseudo-Riemannian manifolds." Monatshefte f�r Mathematik 124, no. 1 (March 1997): 17–34. http://dx.doi.org/10.1007/bf01320735.

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16

García-Río, E., M. E. Vázquez-Abal, and R. Vázquez-Lorenzo. "Nonsymmetric Osserman pseudo-Riemannian manifolds." Proceedings of the American Mathematical Society 126, no. 9 (1998): 2771–78. http://dx.doi.org/10.1090/s0002-9939-98-04666-8.

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17

GILKEY, P., and S. NIKČEVIĆ. "PSEUDO-RIEMANNIAN JACOBI–VIDEV MANIFOLDS." International Journal of Geometric Methods in Modern Physics 04, no. 05 (August 2007): 727–38. http://dx.doi.org/10.1142/s0219887807002272.

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We exhibit several families of Jacobi–Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi–Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.

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18

Wolf, Joseph A. "Flat homogeneous pseudo-Riemannian manifolds." Geometriae Dedicata 57, no. 1 (August 1995): 111–20. http://dx.doi.org/10.1007/bf01264064.

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19

Patrangenaru, Victor. "Locally homogeneous pseudo-Riemannian manifolds." Journal of Geometry and Physics 17, no. 1 (September 1995): 59–72. http://dx.doi.org/10.1016/0393-0440(94)00040-b.

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20

Blau, Matthias. "Symmetries and pseudo-Riemannian manifolds." Reports on Mathematical Physics 25, no. 1 (February 1988): 109–16. http://dx.doi.org/10.1016/0034-4877(88)90045-6.

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21

Chen, Zhiqi, and Joseph A. Wolf. "Pseudo-Riemannian weakly symmetric manifolds." Annals of Global Analysis and Geometry 41, no. 3 (August 20, 2011): 381–90. http://dx.doi.org/10.1007/s10455-011-9291-z.

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22

MANTICA, CARLO ALBERTO, and YOUNG JIN SUH. "RECURRENT Z FORMS ON RIEMANNIAN AND KAEHLER MANIFOLDS." International Journal of Geometric Methods in Modern Physics 09, no. 07 (September 7, 2012): 1250059. http://dx.doi.org/10.1142/s0219887812500594.

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In this paper, we introduce a new kind of Riemannian manifold that generalize the concept of weakly Z-symmetric and pseudo-Z-symmetric manifolds. First a Z form associated to the Z tensor is defined. Then the notion of Z recurrent form is introduced. We take into consideration Riemannian manifolds in which the Z form is recurrent. This kind of manifold is named ( ZRF )n. The main result of the paper is that the closedness property of the associated covector is achieved also for rank (Zkl) > 2. Thus the existence of a proper concircular vector in the conformally harmonic case and the form of the Ricci tensor are confirmed for( ZRF )n manifolds with rank (Zkl) > 2. This includes and enlarges the corresponding results already proven for pseudo-Z-symmetric ( PZS )n and weakly Z-symmetric manifolds ( WZS )n in the case of non-singular Z tensor. In the last sections we study special conformally flat ( ZRF )n and give a brief account of Z recurrent forms on Kaehler manifolds.

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23

Andreeva, Tatiana A., Dmitry N. Oskorbin, and Evgeny D. Rodionov. "Investigation of conformally killing vector fields on 5-dimensional 2-symmetric lorentzian manifolds." Yugra State University Bulletin 60, no. 1 (December 23, 2021): 17–22. http://dx.doi.org/10.17816/byusu20210117-22.

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Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investigated in cases k=2,3 by D.V. Alekseevsky, A.S. Galaev and others. For arbitrary k, non-trivial examples of such spaces are known: generalized Kachen - Wallach manifolds. In the case of small dimensions, these spaces and Killing vector fields on them were studied by D.N. Oskorbin, E.D. Rodionov, and I.V. Ernst with the helpof systems of computer mathematics. In this paper, using the Sagemath SCM, we investigate conformally Killing vector fields on five-dimensional indecomposable 2- symmetric Lorentzian manifolds, and construct an algorithm for their computation.

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24

Shandra, Igor G., and Josef Mikeš. "Geodesic Mappings of Semi-Riemannian Manifolds with a Degenerate Metric." Mathematics 10, no. 1 (January 5, 2022): 154. http://dx.doi.org/10.3390/math10010154.

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This article introduces the concept of geodesic mappings of manifolds with idempotent pseudo-connections. The basic equations of canonical geodesic mappings of manifolds with completely idempotent pseudo-connectivity and semi-Riemannian manifolds with a degenerate metric are obtained. It is proved that semi-Riemannian manifolds admitting concircular fields admit completely canonical geodesic mappings and form a closed class with respect to these mappings.

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25

Değirmenci, Nedim, and Şenay Karapazar. "Seiberg-Witten Equations on Pseudo-Riemannian Spinc Manifolds With Neutral Signature." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 1 (May 1, 2012): 73–88. http://dx.doi.org/10.2478/v10309-012-0006-7.

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Abstract Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature whose structure groups are SO+(2; 2). We prove that such manifolds have pseudo-Riemannian spinc structure. We construct spinor bundle S and half-spinor bundles S+ and S- on these manifolds. For the first Seiberg-Witten equation we define Dirac operator on these bundles. Due to the neutral metric self-duality of a 2-form is meaningful and it enables us to write down second Seiberg-Witten equation. Lastly we write down the explicit forms of these equations on 4-dimensional at space

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26

Andrejic, Vladica. "Quasi-special Osserman manifolds." Filomat 28, no. 3 (2014): 623–33. http://dx.doi.org/10.2298/fil1403623a.

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In this paper we deal with a pseudo-Riemannian Osserman curvature tensor whose reduced Jacobi operator is diagonalizable with exactly two distinct eigenvalues. The main result gives new insight into the theory of the duality principle for pseudo-Riemannian Osserman manifolds. We concern with special Osserman curvature tensor and propose new ways to exclude some additional duality principle conditions from its definition.

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27

Vylegzhanin, D. V., P. N. Klepikov, and O. P. Khromova. "Eigenvalues of the Ricci Operator on Four-Dimensional Locally Homogeneous (Pseudo)Riemannian Manifolds with a Four-Dimensional Isotropy Subgroup." Izvestiya of Altai State University, no. 1(117) (March 17, 2021): 93–96. http://dx.doi.org/10.14258/izvasu(2021)1-15.

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The problem of restoring a (pseudo)Riemannian manifold from a given Ricci operator was studied in the papers of many mathematicians. This problem was solved by O. Kowalski and S. Nikcevic for the case of three-dimensional locally homogeneous Riemannian manifolds. The work of G. Calvaruso and O. Kowalski contains the answer to the question above for the case of three –dimensional locally homogeneous Lorentzian manifolds. For the four-dimensional case, similar studies were carried out only in the case of Lie groups with a left-invariant Riemannian metric. The works of A.G. Kremlyov and Yu.G. Nikonorov presented the possible signatures of the eigenvalues of the Ricci operator. However, the question of recovering a four-dimensional Lie group with a left-invariant Riemannian metric from a given Ricci operator remains open. This paper is devoted to the study of the eigenvalues of the Ricci operator on four-dimensional locally homogeneous (pseudo)Riemannian manifolds with a four-dimensional isotropy subgroup. An algorithm for calculating the eigenvalues of the Ricci operator is presented. A theorem on the restoration of such manifolds from a given Ricci operator is proved. It is established that such possibility can happen only in the case when the prescribed operator is diagonalizable and has a unique eigenvalue of multiplicity four.

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28

SALIMOV, A. A., M. ISCAN, and K. AKBULUT. "NOTES ON PARA-NORDEN–WALKER 4-MANIFOLDS." International Journal of Geometric Methods in Modern Physics 07, no. 08 (December 2010): 1331–47. http://dx.doi.org/10.1142/s021988781000483x.

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A Walker 4-manifold is a pseudo-Riemannian manifold, (M4, g) of neutral signature, which admits a field of parallel null 2-plane. The main purpose of the present paper is to study almost paracomplex structures on 4-dimensional Walker manifolds. We discuss sequently the problem of integrability, para-Kähler (paraholomorphic), quasi-para-Kähler and isotropic para-Kähler conditions for these structures. The curvature properties for para-Norden–Walker metrics with respect to the almost paracomplex structure and some properties of para-Norden–Walker metrics in context of almost product Riemannian manifolds are also investigated. Also, we discuss the Einstein conditions for these structures.

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29

Hui-Li, Liu. "Minimal immersion of pseudo-Riemannian manifolds." Tsukuba Journal of Mathematics 16, no. 1 (June 1992): 1–10. http://dx.doi.org/10.21099/tkbjm/1496161826.

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30

Gilkey, P., and S. Nik evi. "Complete curvature homogeneous pseudo-Riemannian manifolds." Classical and Quantum Gravity 21, no. 15 (July 15, 2004): 3755–70. http://dx.doi.org/10.1088/0264-9381/21/15/009.

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31

Ikemakhen, Aziz. "Parallel spinors on pseudo-Riemannian manifolds." Journal of Geometry and Physics 56, no. 9 (September 2006): 1473–83. http://dx.doi.org/10.1016/j.geomphys.2005.07.005.

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32

Dong, Yuxin, and Ye-Lin Ou. "Biharmonic submanifolds of pseudo-Riemannian manifolds." Journal of Geometry and Physics 112 (February 2017): 252–62. http://dx.doi.org/10.1016/j.geomphys.2016.11.019.

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33

Aminova, A. V. "Pseudo-Riemannian manifolds with common geodesics." Russian Mathematical Surveys 48, no. 2 (April 30, 1993): 105–60. http://dx.doi.org/10.1070/rm1993v048n02abeh001014.

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34

Chen, Zhiqi, and Joseph A. Wolf. "Semisimple weakly symmetric pseudo-Riemannian manifolds." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 88, no. 2 (August 29, 2018): 331–69. http://dx.doi.org/10.1007/s12188-018-0195-8.

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35

Gilkey, Peter B., Raina Ivanova, and Tan Zhang. "Szabo Osserman IP pseudo-Riemannian manifolds." Publicationes Mathematicae Debrecen 62, no. 3-4 (April 1, 2003): 387–401. http://dx.doi.org/10.5486/pmd.2003.2816.

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36

Rovenski, Vladimir, and Tomasz Zawadzki. "The Einstein-Hilbert Type Action on Pseudo-Riemannian Almost-Product Manifolds." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 1 (March 25, 2019): 86–121. http://dx.doi.org/10.15407/mag15.01.086.

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37

BLAŽIĆ, NOVICA, PETER GILKEY, STANA NIKČEVIĆ, and IVA STAVROV. "CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS." International Journal of Geometric Methods in Modern Physics 05, no. 07 (November 2008): 1191–204. http://dx.doi.org/10.1142/s0219887808003259.

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We show the existence of a modified Cliff(1,1)-structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2). We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we prove some new results regarding (Jordan) Osserman manifolds.

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38

Calvaruso, Giovanni, and Anna Fino. "Four-dimensional pseudo-Riemannian homogeneous Ricci solitons." International Journal of Geometric Methods in Modern Physics 12, no. 05 (May 2015): 1550056. http://dx.doi.org/10.1142/s0219887815500565.

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We consider four-dimensional homogeneous pseudo-Riemannian manifolds with non-trivial isotropy and completely classify the cases giving rise to non-trivial homogeneous Ricci solitons. In particular, we show the existence of non-compact homogeneous (and also invariant) pseudo-Riemannian Ricci solitons which are not isometric to solvmanifolds, and of conformally flat homogeneous pseudo-Riemannian Ricci solitons which are not symmetric.

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39

ṢAHIN, BAYRAM. "SLANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 02 (December 5, 2012): 1250080. http://dx.doi.org/10.1142/s0219887812500806.

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We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficient conditions for slant Riemannian maps to be totally geodesic. Moreover, we relate the notion of slant Riemannian maps to the notion of pseudo horizontally weakly conformal (PHWC) maps which are useful for proving various complex-analytic properties of stable harmonic maps from complex projective space.

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40

Shandra and Mikeš. "Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields." Mathematics 7, no. 8 (August 1, 2019): 692. http://dx.doi.org/10.3390/math7080692.

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In the present paper, we study geodesic mappings of special pseudo-Riemannian manifolds called V n ( K ) -spaces. We prove that the set of solutions of the system of equations of geodesic mappings on V n ( K ) -spaces forms a special Jordan algebra and the set of solutions generated by concircular fields is an ideal of this algebra. We show that pseudo-Riemannian manifolds admitting a concircular field of the basic type form the class of manifolds closed with respect to the geodesic mappings.

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41

Haji-Badali, Ali, and Amirhesam Zaeim. "Commutative curvature operators over four-dimensional homogeneous manifolds." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550123. http://dx.doi.org/10.1142/s0219887815501236.

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Four-dimensional pseudo-Riemannian homogeneous spaces whose isotropy is non-trivial with commuting curvature operators have been studied. The only example of homogeneous Einstein four-manifold which is curvature-Ricci commuting but not semi-symmetric has been presented. Non-trivial examples of semi-symmetric homogeneous four-manifolds which are not locally symmetric, also Jacobi–Jacobi commuting manifolds which are not flat have been presented.

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42

Erken, İrem, and Cengizhan Murathan. "Biharmonic pseudo-Riemannian submersions from 3-manifolds." Filomat 32, no. 2 (2018): 543–52. http://dx.doi.org/10.2298/fil1802543e.

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Park, Kwang-Soon. "Almost h-semi-slant Riemannian maps to almost quaternionic Hermitian manifolds." Communications in Contemporary Mathematics 17, no. 06 (October 29, 2015): 1550008. http://dx.doi.org/10.1142/s021919971550008x.

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We introduce the notions of almost h-slant Riemannian maps, almost h-semi-invariant Riemannian maps, and almost h-semi-slant Riemannian maps from Riemannian manifolds to almost quaternionic Hermitian manifolds. We investigate the harmonicity of such maps and the geometry of distributions. We also find the conditions for such maps to be totally geodesic, relate the notion of pseudo-horizontally weakly conformal maps to those notions, and give some examples of such maps.

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44

BONOME, Agustin, Regina CASTRO, Eduardo GARCÍA-RÍO, Luis HERVELLA, and Ramón VÁZQUEZ-LORENZO. "Pseudo-Riemannian manifolds with simple Jacobi operators." Journal of the Mathematical Society of Japan 54, no. 4 (October 2002): 847–75. http://dx.doi.org/10.2969/jmsj/1191591994.

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Bocheński, Maciej, Piotr Jastrzębski, and Aleksy Tralle. "On locally homogeneous compact pseudo-Riemannian manifolds." Colloquium Mathematicum 150, no. 1 (2017): 135–39. http://dx.doi.org/10.4064/cm7139s-1-2017.

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46

Calvaruso, Giovanni, and Amirhesam Zaeim. "Conformally flat homogeneous pseudo-Riemannian four-manifolds." Tohoku Mathematical Journal 66, no. 1 (2014): 31–54. http://dx.doi.org/10.2748/tmj/1396875661.

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Galaev, Anton S. "Holonomy algebras of Einstein pseudo-Riemannian manifolds." Journal of the London Mathematical Society 98, no. 2 (May 1, 2018): 393–415. http://dx.doi.org/10.1112/jlms.12135.

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Galaev, A. S. "Pseudo-Riemannian manifolds with recurrent spinor fields." Siberian Mathematical Journal 54, no. 4 (July 2013): 604–13. http://dx.doi.org/10.1134/s0037446613040034.

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Gilkey, Peter B., Raina Ivanova, and Tan Zhang. "Higher-order Jordan Osserman pseudo-Riemannian manifolds." Classical and Quantum Gravity 19, no. 17 (August 13, 2002): 4543–51. http://dx.doi.org/10.1088/0264-9381/19/17/306.

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Kath, I. "G2(2)∗-structures on pseudo-Riemannian manifolds." Journal of Geometry and Physics 27, no. 3-4 (September 1998): 155–77. http://dx.doi.org/10.1016/s0393-0440(97)00073-9.

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