Relevant bibliographies by topics / Pseudo-Riemannian manifolds

Academic literature on the topic 'Pseudo-Riemannian manifolds'

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Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Pseudo-Riemannian manifolds"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Pseudo-Riemannian manifolds"

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Dunn, Corey. "Curvature homogeneous pseudo-Riemannian manifolds /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1188874491&sid=3&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 146-147). Also available for download via the World Wide Web; free to University of Oregon users.
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Catalano, Domenico Antonino. "Concircular diffeomorphisms of pseudo-Riemannian manifolds /." [S.l.] : [s.n.], 1999. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13064.

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Friswell, Robert Michael. "Harmonic vector fields on pseudo-Riemannian manifolds." Thesis, University of York, 2014. http://etheses.whiterose.ac.uk/7878/.

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This thesis generalises the theory of harmonic vector fields to the non-compact pseudo- Riemannian case. After introducing the required background theory we consider the first variation of the local energies to find the Euler-Lagrange equations for this new case. We then introduce a natural closed conformal gradient field on pseudo-Riemannian warped products and find the Euler-Lagrange equations for harmonic closed conformal vector fields of this sort. We then give examples of such harmonic closed conformal fields, this leads to a harmonic vector fields on a 2-sphere with a rotationally symmetric singular metric. The harmonic conformal gradient fields on all hyperquadrics are then categorised up to con- gruence. The harmonic Killing fields on the 2-dimensional hyperquadrics are found, and shown to be unique up to congruence.
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Botros, Amir A. "GEODESICS IN LORENTZIAN MANIFOLDS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/275.

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We present an extension of Geodesics in Lorentzian Manifolds (Semi-Riemannian Manifolds or pseudo-Riemannian Manifolds ). A geodesic on a Riemannian manifold is, locally, a length minimizing curve. On the other hand, geodesics in Lorentzian manifolds can be viewed as a distance between ``events''. They are no longer distance minimizing (instead, some are distance maximizing) and our goal is to illustrate over what time parameter geodesics in Lorentzian manifolds are defined. If all geodesics in timelike or spacelike or lightlike are defined for infinite time, then the manifold is called ``geodesically complete'', or simply, ``complete''. It is easy to show that the magnitude of a geodesic is constant, so one can characterize geodesics in terms of their causal character: if this magnitude is negative, the geodesic is called timelike. If this magnitude is positive, then it is spacelike. If this magnitude is 0, then it is called lightlike or null. Geodesic completeness can be considered by only considering one causal character to produce the notions of spacelike complete, timelike complete, and null or lightlike complete. We illustrate that some of the notions are inequivalent.
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Globke, Wolfgang [Verfasser], and O. [Akademischer Betreuer] Baues. "Holonomy Groups of Flat Pseudo-Riemannian Homogeneous Manifolds / Wolfgang Globke. Betreuer: O. Baues." Karlsruhe : KIT-Bibliothek, 2011. http://d-nb.info/1014279771/34.

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Tsonev, Dragomir. "Realisation of holonomy algebras on pseudo-Riemannian manifolds by means of Manakov operators." Thesis, Loughborough University, 2013. https://dspace.lboro.ac.uk/2134/12465.

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In the present thesis we construct a new class of holonomy algebras in pseudo-Riemannian geometry. Starting from a smooth connected manifold M, we consider its (1;1)-tensor fields acting on the tangent spaces. We then prove that there exists a class of pseudo- Riemannian metrics g on M such that the (1;1)-tensor fields are g-self adjoint and their centralisers in the Lie algebra so(g) are holonomy algebras for the Levi-Civita connection of g. Our construction is elaborated with the aid of Manakov operators and holds for any signature of the metric g.
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Lischewski, Andree. "Geometric constructions and structures associated with twistor spinors on pseudo-Riemannian conformal manifolds." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17132.

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Die Arbeit untersucht lokale Geometrien, die Twistorspinoren zulassen auf pseudo-Riemannschen Mannigfaltigkeiten beliebiger Signatur. Hierzu entwickeln wir die benötigten Methoden, nämlich das konforme Traktorkalkül, welches eine konform-invariante Beschreibung von Twistorspinoren als parallele Objekte ermöglicht, weiter. In diesem Zusammenhang ist unser erstes zentrales Resultat ein Klassifikationssatz für konforme Strukturen, deren Holonomiegruppen einen total ausgearteten Unterraum beliebiger Dimension invariant lassen. Hierauf aufbauend können wir einen partiellen Klassifikationssatz für konforme Strukturen mit Twistorspinoren beweisen. Weiterhin studieren wir die Nullstellenmenge eines Twistorspinors unter Nutzung der Theorie der Orbitzerlegungen für parabolische Geometrien. Wir können die lokale geometrische Struktur der Nullstellenmenge vollständig beschreiben und zeigen, dass lokal jeder Twistorspinor mit Nullstelle konform äquivalent zu einem parallelem Spinor ist. Eine Anwendung dieser Resultate auf niedrig-dimensionale Split-Signaturen führt zu einer vollständigen geometrischen Beschreibung von Mannigfaltigkeiten mit nicht-generischen Twistorspinoren in den Signaturen (3,2) und (3,3) durch parallele Spinoren, was die schon bekannte Analyse des generischen Falls komplementiert. Darüberhinaus wenden wir das Traktorkalkül an, um einer konformen Spin- Mannigfaltigkeit auf natürliche Weise eine konforme Superalgebra zuzuordnen. Dieser Zugang führt zu verschiedenen Resultaten, die algebraische Eigenschaften dieser Superalgebra mit speziellen Geometrien auf der zugrundeliegenden Mannigfaltigkeit in Verbindung bringen. Weiterhin erhält man so neue Konstruktionsprinzipien für Twistorspinoren und konforme Killingformen. Zuletzt führen wir den Begriff der konformen Spin-c-Geometrie ein. Unter anderem liefern spezielle Spin-c-Twistorspinoren eine neue Charakterisierung von Fefferman-Räumen.
The present thesis studies local geometries admitting twistor spinors on pseudo- Riemannian manifolds of arbitrary signature. To this end, we refine and extend the necessary machinery of first prolongation of conformal structures and conformal tractor calculus which allows a conformally-invariant description of twistor spinors as parallel objects. In this context, our first main theorem is a classification result for conformal geometries whose conformal holonomy group admits a totally degenerate invariant subspace of arbitrary dimension. Based on this we are able to prove a partial classification result for conformal structures admitting twistor spinors. Moreover, we study the zero set of a twistor spinor using the theory of curved orbit decompositions for parabolic geometries. We can completely describe the local geometric structure of the zero set and show that locally every twistor spinor with zero is equivalent to a parallel spinor off the zero set. An application of these results in low-dimensional split-signatures leads to a complete geometric description of manifolds admitting non-generic twistor spinors in signatures (3,2) and (3,3) in terms of parallel spinors which complements the well-known analysis of the generic case. Moreover, we apply tractor calculus for the construction of a conformal superalgebra naturally associated to a conformal spin structure. This approach leads to various results linking algebraic properties of the superalgebra to special geometric structures on the underlying manifold. It also exhibits new construction principles for twistor spinors and conformal Killing forms. Finally, we introduce and elaborate on the notion of conformal Spin-c-geometry. Among other aspects, this gives rise to a new characterization of Fefferman spaces in terms of distinguished Spin-c-twistor spinors.
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Lärz, Kordian. "Global aspects of holonomy in pseudo-Riemannian geometry." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16363.

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In dieser Arbeit untersuchen wir die Interaktion von Holonomie und der globalen Geometrie von Lorentzmannigfaltigkeiten und pseudo-Riemannschen Untermannigfaltigkeiten in Räumen konstanter Krümmung. Insbesondere konstruieren wir schwach irreduzible, reduzible Lorentzmetriken auf den Totalräumen von gewissen Kreisbündeln, was zu einer Konstruktionsmethode von Lorentzmannigfaltigkeiten mit vorgegebener Holonomiedarstellung führt. Danach führen wir eine Bochnertechnik für die Lorentzmannigfaltigkeiten ein, die ein nirgends verschwindendes, paralleles, lichtartiges Vektorfeld zulassen, dessen orthogonale Distribution kompakte Blätter hat. Schließlich klassifizieren wir normale Holonomiedarstellungen von raumartigen Untermannigfaltigkeiten in Räumen konstanter Krümmung und verallgemeinern die Klassifikation eine größere Klasse von Untermannigfaltigkeiten.
In this thesis we study the interaction of holonomy and the global geometry of Lorentzian manifolds and pseudo-Riemannian submanifolds in spaces of constant curvature. In particular, we construct weakly irreducible, reducible Lorentzian metrics on the total spaces of certain circle bundles leading to a construction of Lorentzian manifolds with specified holonomy representations. Then we introduce a Bochner technique for Lorentzian manifolds admitting a nowhere vanishing parallel lightlike vector field whose orthogonal distribution has compact leaves. Finally, we classify normal holonomy representations of spacelike submanifolds in spaces of constant curvature and extend the classification to more general submanifolds.
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Fama, Christopher J., and -. "Non-smooth differential geometry of pseudo-Riemannian manifolds: Boundary and geodesic structure of gravitational wave space-times in mathematical relativity." The Australian National University. School of Mathematical Sciences, 1998. http://thesis.anu.edu.au./public/adt-ANU20010907.161849.

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[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.
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Lischewski, Andree [Verfasser], Helga [Akademischer Betreuer] Baum, Hans Bert [Akademischer Betreuer] Rademacher, and José [Akademischer Betreuer] Figueroa-O'Farrill. "Geometric constructions and structures associated with twistor spinors on pseudo-Riemannian conformal manifolds / Andree Lischewski. Gutachter: Helga Baum ; Hans Bert Rademacher ; José Figueroa-O'Farrill." Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://d-nb.info/1067484841/34.

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Books on the topic "Pseudo-Riemannian manifolds"

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Minimal submanifolds in pseudo-Riemannian geometry. New Jersey: World Scientific, 2011.

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The geometry of curvature homogenous pseudo-Riemannian manifolds. London: Imperial College Press, 2007.

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Chen, Bang-Yen. Pseudo-riemannian geometry, [delta]-invariants and applications. Singapore: World Scientific, 2011.

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Chen, Bang-Yen. Pseudo-riemannian geometry, [delta]-invariants and applications. Singapore: World Scientific, 2011.

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1940-, Alekseevskiĭ Dmitriĭ Vladimirovich, and Baum Helga 1954-, eds. Recent developments in pseudo-Riemannian geometry. Zürich: European Mathematical Society, 2008.

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Null Curves and Hypersurfaces of Semi-riemannian Manifolds. World Scientific Publishing Company, 2007.

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Gilkey, Peter B. The Geometry of Curvature Homogeneous Pseudo-riemannian Manifolds (ICP Advanced Texts in Mathematics) (Icp Advanced Texts in Mathematics). Imperial College Press, 2007.

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Kachelriess, Michael. Spacetime symmetries. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0006.

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This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.
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Book chapters on the topic "Pseudo-Riemannian manifolds"

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Girbau, Joan, and Lluís Bruna. "Pseudo-Riemannian Manifolds." In Stability by Linearization of Einstein’s Field Equation, 1–17. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0304-1_1.

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Muniz Oliva, Waldyr. "3. Pseudo-Riemannian manifolds." In Lecture Notes in Mathematics, 23–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-45795-4_4.

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Calvaruso, Giovanni, and Marco Castrillón López. "Locally Homogeneous Pseudo-Riemannian Manifolds." In Developments in Mathematics, 59–90. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18152-9_3.

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Anastasiei, M., Gabriela Ciobanu, and I. Gottlieb. "Contraforms on Pseudo-Riemannian Manifolds." In Finsler and Lagrange Geometries, 249–58. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0405-2_28.

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Calvaruso, Giovanni, and Marco Castrillón López. "Where All This Fails: Non-reductive Homogeneous Pseudo-Riemannian Manifolds." In Developments in Mathematics, 197–221. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18152-9_7.

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Lumiste, Ülo. "Isometric Semiparallel Immersions of Two-Dimensional Riemannian Manifolds into Pseudo-Euclidean Spaces." In New Developments in Differential Geometry, Budapest 1996, 243–64. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-5276-1_17.

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Das, Anadijiban, and Andrew DeBenedictis. "The Pseudo-Riemannian Space-Time Manifold M4." In The General Theory of Relativity, 105–228. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3658-4_2.

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Crumeyrolle, Albert. "The Clifford Algebra and the Clifford Bundle of a Pseudo-Riemannian Manifold. Existence Conditions for Spinor Structures." In Orthogonal and Symplectic Clifford Algebras, 180–203. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-015-7877-6_14.

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"Pseudo-Riemannian Manifolds." In Pseudo-Riemannian Geometry, δ-Invariants and Applications, 1–24. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814329644_0001.

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Martin, Daniel. "Pseudo-Riemannian and Riemannian manifolds." In Manifold Theory, 180–238. Elsevier, 2002. http://dx.doi.org/10.1533/9780857099631.180.

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Conference papers on the topic "Pseudo-Riemannian manifolds"

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Kath, Ines. "Parallel Pure Spinors on Pseudo-Riemannian Manifolds." In Differential Geometry in Honor of Professor S S Chern. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792051_0008.

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SÁNCHEZ-RODRÍGUEZ, IGNACIO. "G-STRUCTURES DEFINED ON PSEUDO-RIEMANNIAN MANIFOLDS." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0035.

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Alekseevsky, D. V., V. Cortés, Oscar J. Garay, Marisa Fernández, Luis Carlos de Andrés, and Luis Ugarte. "On pseudo-Riemannian manifolds with many Killing spinors." In SPECIAL METRICS AND SUPERSYMMETRY: Proceedings of the Workshop on Geometry and Physics: Special Metrics and Supersymmetry. AIP, 2009. http://dx.doi.org/10.1063/1.3089206.

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Berezovski, V. E., J. Mikeš, and A. Vanžurová. "Canonical almost geodesics mappings of type $\tilde{\pi}_1$ onto pseudo-Riemannian manifolds." In Proceedings of the 10th International Conference on DGA2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790613_0007.

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GILKEY, PETER B., and STANA NIKČEVIĆ. "COMPLETE K-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS 0-MODELED ON AN INDECOMPOSIBLE SYMMETRIC SPACE." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0007.

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Mikeš, Josef, Sergey Stepanov, and Irena Hinterleitner. "Projective mappings and dimensions of vector spaces of three types of Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733381.

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Reports on the topic "Pseudo-Riemannian manifolds"

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Dušek, Zdenek. Examples of Pseudo-Riemannian G.O. Manifolds. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-144-155.

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Zohrehvand, Mosayeb. IFHP Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Pseudo-Riemannian Metrics. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2020. http://dx.doi.org/10.7546/crabs.2020.02.04.

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