Log in

Relevant bibliographies by topics / Harmonic-Einstein manifold / Journal articles

Journal articles on the topic 'Harmonic-Einstein manifold'

To see the other types of publications on this topic, follow the link: Harmonic-Einstein manifold.

Author: Grafiati

Published: 9 March 2023

Last updated: 11 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 28 journal articles for your research on the topic 'Harmonic-Einstein manifold.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

HE, QUN, and YI-BING SHEN. "SOME RESULTS ON HARMONIC MAPS FOR FINSLER MANIFOLDS." International Journal of Mathematics 16, no. 09 (October 2005): 1017–31. http://dx.doi.org/10.1142/s0129167x05003211.

Full text

Abstract:

By simplifying the first and the second variation formulas of the energy functional and generalizing the Weitzenböck formula, we study the stability and the rigidity of harmonic maps between Finsler manifolds. It is proved that any nondegenerate harmonic map from a compact Einstein Riemannian manifold with nonnegative scalar curvature to a Berwald manifold with nonpositive flag curvature is totally geodesic and there is no nondegenerate stable harmonic map from a Riemannian unit sphere Sn (n > 2) to any Finsler manifold.

APA, Harvard, Vancouver, ISO, and other styles

2

VILLE, MARINA. "HARMONIC MORPHISMS FROM EINSTEIN 4-MANIFOLDS TO RIEMANN SURFACES." International Journal of Mathematics 14, no. 03 (May 2003): 327–37. http://dx.doi.org/10.1142/s0129167x0300179x.

Full text

Abstract:

If M and N are Riemannian manifolds, a harmonic morphism f : M → N is a map which pulls back local harmonic functions on N to local harmonic functions on M. If M is an Einstein 4-manifold and N is a Riemann surface, John Wood showed that such an f is holomorphic w.r.t. some integrable complex Hermitian structure defined on M away from the singular points of f. In this paper we extend this complex structure to the entire manifold M. It follows that there are no non-constant harmonic morphisms from [Formula: see text] or [Formula: see text] to a Riemann surface. The proof relies heavily on the real analyticity of the whole situation. We conclude by an example of a non-constant harmonic morphism from [Formula: see text] to [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

3

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

4

Shenawy, Sameh, Carlo Alberto Mantica, Luca Guido Molinari, and Nasser Bin Turki. "A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor." Mathematics 10, no. 10 (May 18, 2022): 1731. http://dx.doi.org/10.3390/math10101731.

Full text

Abstract:

Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a λ,n+m-Einstein manifold M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces to a perfect fluid generalized Robertson–Walker spacetime with Einstein fibers. Finally, M,g,w reduces to a perfect fluid manifold if φ=−m∇lnw is a φRic-vector field on M and to an Einstein manifold if ψ=∇w is a ψRic-vector field on M. Some consequences of these results are considered.

APA, Harvard, Vancouver, ISO, and other styles

5

WOOD, JOHN C. "HARMONIC MORPHISMS AND HERMITIAN STRUCTURES ON EINSTEIN 4-MANIFOLDS." International Journal of Mathematics 03, no. 03 (June 1992): 415–39. http://dx.doi.org/10.1142/s0129167x92000187.

Full text

Abstract:

We show that a submersive harmonic morphism from an orientable Einstein 4-manifold M4 to a Riemann surface, or a conformal foliation of M4 by minimal surfaces, determines an (integrable) Hermitian structure with respect to which it is holomorphic. Conversely, any nowhere-Kähler Hermitian structure of an orientable anti-self-dual Einstein 4-manifold arises locally in this way. In the case M4=ℝ4 we show that a Hermitian structure, viewed as a map into S2, is a harmonic morphism; in this case and for S4, [Formula: see text] we determine all (submersive) harmonic morphisms to surfaces locally, and, assuming a non-degeneracy condition on the critical points, globally.

APA, Harvard, Vancouver, ISO, and other styles

6

Shojaee, Neda, and Morteza Mirmohammad Rezaii. "Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure." Advances in Pure and Applied Mathematics 9, no. 2 (April 1, 2018): 131–41. http://dx.doi.org/10.1515/apam-2016-0099.

Full text

Abstract:

AbstractIn the present work, the harmonic vector field is defined on closed Finsler measure spaces through different approaches. At first, the weighted harmonic vector field is obtained as the solution space of a PDE system. Then a suitable Dirichlet energy functional is introduced. A σ-harmonic vector field is considered as the critical point of related action. It is proved that a σ-harmonic vector field on a closed Finsler space with an extra unit norm condition is an eigenvector of the defined Laplacian operator on vector fields. Moreover, we prove that a unit weighted harmonic vector field on a closed generalized Einstein manifold is a σ-harmonic vector field.

APA, Harvard, Vancouver, ISO, and other styles

7

Beheshti, Shabnam, and Shadi Tahvildar-Zadeh. "Integrability and vesture for harmonic maps into symmetric spaces." Reviews in Mathematical Physics 28, no. 03 (April 2016): 1650006. http://dx.doi.org/10.1142/s0129055x16500069.

Full text

Abstract:

After formulating the notion of integrability for axially symmetric harmonic maps from [Formula: see text] into symmetric spaces, we give a complete and rigorous proof that, subject to some mild restrictions on the target, all such maps are integrable. Furthermore, we prove that a variant of the inverse scattering method, called vesture (dressing) can always be used to generate new solutions for the harmonic map equations starting from any given solution. In particular, we show that the problem of finding [Formula: see text]-solitonic harmonic maps into a non-compact Grassmann manifold [Formula: see text] is completely reducible via the vesture (dressing) method to a problem in linear algebra which we prove is solvable in general. We illustrate this method, and establish its agreement with previously known special cases, by explicitly computing a 1-solitonic harmonic map for the two cases [Formula: see text] and [Formula: see text] and showing that the family of solutions obtained in each case contains respectively the Kerr family of solutions to the Einstein vacuum equations, and the Kerr–Newman family of solutions to the Einstein–Maxwell equations in the hyperextreme sector of the corresponding parameters.

APA, Harvard, Vancouver, ISO, and other styles

8

Deshmukh, Sharief, and Ibrahim Al-Dayel. "Concircularity on GRW-space-times and conformally flat spaces." International Journal of Geometric Methods in Modern Physics 18, no. 08 (May 8, 2021): 2150132. http://dx.doi.org/10.1142/s0219887821501322.

Full text

Abstract:

There are two smooth functions [Formula: see text] and [Formula: see text] associated to a nontrivial concircular vector field [Formula: see text] on a connected Riemannian manifold [Formula: see text], called potential function and connecting function. In this paper, we show that presence of a timelike nontrivial concircular vector field influences the geometry of generalized Robertson–Walker space-times. We use a timelike concircular vector field [Formula: see text] on an [Formula: see text] -dimensional connected conformally flat Lorentzian manifold, [Formula: see text], to find a characterization of generalized Robertson–Walker space-time with fibers Einstein manifolds. It is interesting to note that for [Formula: see text] the concircular vector field annihilates energy-momentum tensor and also that in this case the potential function [Formula: see text] is harmonic. In the second part of this paper, we show that presence of a nontrivial concircular vector field [Formula: see text] with connecting function [Formula: see text] on a complete and connected [Formula: see text] -dimensional conformally flat Riemannian manifold [Formula: see text], [Formula: see text], with Ricci curvature [Formula: see text] non-negative, satisfying [Formula: see text], is necessary and sufficient for [Formula: see text] to be isometric to either a sphere [Formula: see text] or to the Euclidean space [Formula: see text], where [Formula: see text] is the scalar curvature.

APA, Harvard, Vancouver, ISO, and other styles

9

Mantica, Carlo Alberto, and Young Jin Suh. "Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves." International Journal of Geometric Methods in Modern Physics 13, no. 02 (January 26, 2016): 1650015. http://dx.doi.org/10.1142/s0219887816500158.

Full text

Abstract:

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

APA, Harvard, Vancouver, ISO, and other styles

10

Gudmundsson, Sigmundur. "Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds." International Journal of Mathematics 26, no. 01 (January 2015): 1550006. http://dx.doi.org/10.1142/s0129167x15500068.

Full text

Abstract:

We construct four-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not Kähler. We then prove that the Riemannian Lie groups constructed are not Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.

APA, Harvard, Vancouver, ISO, and other styles

11

Franchetti, Guido. "Harmonic spinors on a family of Einstein manifolds." Nonlinearity 31, no. 6 (April 24, 2018): 2419–41. http://dx.doi.org/10.1088/1361-6544/aab0bd.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Catino, Giovanni. "Generalized quasi-Einstein manifolds with harmonic Weyl tensor." Mathematische Zeitschrift 271, no. 3-4 (May 5, 2011): 751–56. http://dx.doi.org/10.1007/s00209-011-0888-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

LeBrun, Claude. "Einstein metrics, harmonic forms, and symplectic four-manifolds." Annals of Global Analysis and Geometry 48, no. 1 (March 11, 2015): 75–85. http://dx.doi.org/10.1007/s10455-015-9458-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Pantilie, Radu, and John C. Wood. "Harmonic morphisms with one-dimensional fibres on Einstein manifolds." Transactions of the American Mathematical Society 354, no. 10 (May 22, 2002): 4229–43. http://dx.doi.org/10.1090/s0002-9947-02-03044-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Azad, H., and M. T. Mustafa. "Harmonic morphisms of warped product type from Einstein manifolds." Archiv der Mathematik 88, no. 4 (March 19, 2007): 368–77. http://dx.doi.org/10.1007/s00013-006-1941-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Hu, Xue. "On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature." Journal of Geometry and Physics 128 (June 2018): 48–57. http://dx.doi.org/10.1016/j.geomphys.2018.02.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Leung, Naichung C., and Tom Y. H. Wan. "Harmonic maps and the topology of conformally compact Einstein manifolds." Mathematical Research Letters 8, no. 6 (2001): 801–12. http://dx.doi.org/10.4310/mrl.2001.v8.n6.a10.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Güler, Sinem, and Uday Chand De. "Generalized quasi-Einstein metrics and applications on generalized Robertson–Walker spacetimes." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 083501. http://dx.doi.org/10.1063/5.0086836.

Full text

Abstract:

In this paper, we study generalized quasi-Einstein manifolds ( M n, g, V, λ) satisfying certain geometric conditions on its potential vector field V whenever it is harmonic, conformal, and parallel. First, we construct some integral formulas and obtain some triviality results. Then, we find some necessary conditions to construct a quasi-Einstein structure on ( M n, g, V, λ). Moreover, we prove that for any generalized Ricci soliton [Formula: see text], where [Formula: see text] is a generalized Robertson–Walker spacetime metric and the potential field [Formula: see text] is conformal, [Formula: see text] can be considered as the model of perfect fluids in general relativity. Moreover, the fiber ( M, g) also satisfies the quasi-Einstein metric condition. Therefore, the state equation of [Formula: see text] is presented. We also construct some explicit examples of generalized quasi-Einstein metrics by using a four-dimensional Walker metric.

APA, Harvard, Vancouver, ISO, and other styles

19

Negreiros, Caio J. C., Lino Grama, and Neiton P. da Silva. "Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics." Journal of Fixed Point Theory and Applications 10, no. 2 (November 11, 2011): 307–25. http://dx.doi.org/10.1007/s11784-011-0064-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Pantilie, Radu. "Harmonic morphisms with 1-dimensional fibres on 4-dimensional Einstein manifolds." Communications in Analysis and Geometry 10, no. 4 (2002): 779–814. http://dx.doi.org/10.4310/cag.2002.v10.n4.a5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Neto, Benedito Leandro. "Generalized quasi-Einstein manifolds with harmonic anti-self dual Weyl tensor." Archiv der Mathematik 106, no. 5 (April 6, 2016): 489–99. http://dx.doi.org/10.1007/s00013-016-0896-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Aguilar, R. M. "Pseudo-Riemannian Metrics, Kahler-Einstein Metrics on Grauert Tubes and Harmonic Riemannian Manifolds." Quarterly Journal of Mathematics 50, no. 1 (March 1, 2000): 1–17. http://dx.doi.org/10.1093/qmathj/50.1.1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Petersen, Pip, Yashar Akrami, Craig J. Copi, Andrew H. Jaffe, Arthur Kosowsky, Glenn D. Starkman, Andrius Tamosiunas, et al. "Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches." Journal of Cosmology and Astroparticle Physics 2023, no. 01 (January 1, 2023): 030. http://dx.doi.org/10.1088/1475-7516/2023/01/030.

Full text

Abstract:

Abstract The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within ΛCDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

APA, Harvard, Vancouver, ISO, and other styles

24

Shin, Jinwoo. "On the classification of 4-dimensional $$(m,\rho )$$ ( m , ρ ) -quasi-Einstein manifolds with harmonic Weyl curvature." Annals of Global Analysis and Geometry 51, no. 4 (January 30, 2017): 379–99. http://dx.doi.org/10.1007/s10455-017-9542-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Günsen, Seçkin, and Leyla Onat. "ON WARPED PRODUCT MANIFOLDS ADMITTING τ-QUASI RICCI-HARMONIC METRICS." Facta Universitatis, Series: Mathematics and Informatics, August 6, 2022, 333. http://dx.doi.org/10.22190/fumi211212023g.

Full text

Abstract:

In this paper, we study warped product manifolds admitting $\tau$-quasi Ricci-harmonic(RH) metrics. We prove that the metric of the fibre is harmonic Einstein when warped product metric is $\tau$-quasi RH metric. We also provide some conditions for $M$ to be a harmonic Einstein manifold. Finally, we provide necessary and sufficient conditions for a metric $g$ to be $\tau$-quasi RH metric by using a differential equation system.

APA, Harvard, Vancouver, ISO, and other styles

26

Gupta, Punam, and Sanjay Kumar Singh. "Comprehensive quasi-Einstein spacetime with application to general relativity." International Journal of Geometric Methods in Modern Physics 19, no. 02 (November 24, 2021). http://dx.doi.org/10.1142/s0219887822500165.

Full text

Abstract:

The aim of this paper is to extend the notion of all known quasi-Einstein (QE) manifolds like generalized QE, mixed generalized QE manifold, pseudo generalized QE manifold and many more and name it comprehensive QE manifold [Formula: see text]. We investigate some geometric and physical properties of the comprehensive QE manifolds [Formula: see text] under certain conditions. We study the conformal and conharmonic mappings between [Formula: see text] manifolds. Then we examine the [Formula: see text] with harmonic Weyl tensor. We define the manifold of comprehensive quasi-constant curvature and prove that conformally flat [Formula: see text] is manifold of comprehensive quasi-constant curvature and vice versa. We study the general two viscous fluid spacetime [Formula: see text] and find out some important consequences about [Formula: see text]. We study [Formula: see text] with vanishing space matter tensor. Finally, we prove the existence of such manifolds by constructing nontrivial example.

APA, Harvard, Vancouver, ISO, and other styles

27

Yadav, Akhilesh, and Kiran Meena. "Clairaut Riemannian maps whose total manifolds admit a Ricci soliton." International Journal of Geometric Methods in Modern Physics 19, no. 02 (December 13, 2021). http://dx.doi.org/10.1142/s0219887822500244.

Full text

Abstract:

In this paper, we study Clairaut Riemannian maps whose total manifolds admit a Ricci soliton and give a nontrivial example of such Clairaut Riemannian maps. First, we calculate Ricci tensors and scalar curvature of total manifolds of Clairaut Riemannian maps. Then we obtain necessary conditions for the fibers of such Clairaut Riemannian maps to be Einstein and almost Ricci solitons. We also obtain a necessary condition for vector field [Formula: see text] to be conformal, where [Formula: see text] is a geodesic curve on total manifold of Clairaut Riemannian map. Further, we show that if total manifolds of Clairaut Riemannian maps admit a Ricci soliton with the potential mean curvature vector field of [Formula: see text] then the total manifolds of Clairaut Riemannian maps also admit a gradient Ricci soliton and obtain a necessary and sufficient condition for such maps to be harmonic by solving Poisson equation.

APA, Harvard, Vancouver, ISO, and other styles

28

Nakad, Roger, and Mihaela Pilca. "Eigenvalue Estimates of the spincDirac Operator and Harmonic Forms on Kähler-Einstein Manifolds." Symmetry, Integrability and Geometry: Methods and Applications, July 14, 2015. http://dx.doi.org/10.3842/sigma.2015.054.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!