Relevant bibliographies by topics / Pseudo Ricci symmetric manifold

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Academic literature on the topic 'Pseudo Ricci symmetric manifold'

Author: Grafiati
Published: 3 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Pseudo Ricci symmetric manifold"

1

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 (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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Shaikh, Absos Ali, and Shyamal Kumar Hui. "ON PSEUDO CYCLIC RICCI SYMMETRIC MANIFOLDS." Asian-European Journal of Mathematics 02, no. 02 (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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De, U. C., Yanling Han, and Krishanu Mandal. "On para-sasakian manifolds satisfying certain curvature conditions." Filomat 31, no. 7 (2017): 1941–47. http://dx.doi.org/10.2298/fil1707941d.

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In this paper, we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric P-Sasakian manifolds. Next we study P-Sasakian manifolds satisfying the curvature condition S ? R = 0. Finally, we give an example of a 5-dimensional P-Sasakian manifold to verify some results.
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Khromova, O. P., and V. V. Balashchenko. "Symmetric Ricci Flows of Semisymmetric Connections on Three-Dimensional Metrical Lie Groups: An Analysis." Izvestiya of Altai State University, no. 1(129) (March 28, 2023): 141–44. http://dx.doi.org/10.14258/izvasu(2023)1-23.

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The study of Ricci flows, which describe the deformation of (pseudo) Riemannian metrics on a manifold, and their solutions, Ricci solitons, has garnered much attention from mathematicians. However, previous studies have typically focused on manifolds with Levi-Civita connections. This paper breaks new ground by considering manifolds with semisymmetric connections, which also include the Levi-Civita connection. Metric connections with vector torsion, or semisymmetric connections, were first studied by E. Cartan on (pseudo) Riemannian manifolds. Later, K. Yano and I. Agricola studied tensor fields and geodesic lines of such connections, while P.N. Klepikov,
 E.D. Rodionov, and O.P. Khromova considered the Einstein equation of semisymmetric connections on three-dimensional locally homogeneous (pseudo) Riemannian manifolds. Because the Ricci tensor of a semisymmetric connection is not symmetric in general, we focus on studying the symmetric and skew-symmetric parts of the Ricci tensor. Specifically, we investigate symmetric Ricci flows on three-dimensional Lie groups with J. Milnor's left-invariant (pseudo) Riemannian metric and E. Cartan's semisymmetric connection.
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5

Chaturvedi, B. B., and Kunj Bihari Kaushik. "Study of a Projective Ricci Semi-symmetric Nearly Kaehler Manifold." Asian Journal of Mathematics and Computer Research 30, no. 3 (2023): 19–29. http://dx.doi.org/10.56557/ajomcor/2023/v30i38324.

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We inaugurate a new curvature properties of projective curvature tensor in nearly Kaehler manifold. We defined projective Ricci semi-symmetric quasi-Einstein nearly Kaehler manifold, Projective Ricci semisymmetric generalised quasi-Einstein nearly Kaehler manifold and a Projective Ricci semi-symmetric pseudo generalised quasi-Einstein nearly Kaehler manifold and also found some results in the manifold.
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6

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 (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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7

Khan, Mohammad Nazrul Islam, Fatemah Mofarreh, and Abdul Haseeb. "Tangent Bundles of P-Sasakian Manifolds Endowed with a Quarter-Symmetric Metric Connection." Symmetry 15, no. 3 (2023): 753. http://dx.doi.org/10.3390/sym15030753.

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The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle TM. Certain results on a semisymmetric P-Sasakian manifold, generalized recurrent P-Sasakian manifolds, and pseudo-symmetric P-Sasakian manifolds on TM are proved.
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8

MANTICA, CARLO ALBERTO, and YOUNG JIN SUH. "PSEUDO-Q-SYMMETRIC RIEMANNIAN MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 05 (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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9

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 (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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10

De, Krishnendu, Changhwa Woo, and Uday De. "Geometric and physical characterizations of a spacetime concerning a novel curvature tensor." Filomat 38, no. 10 (2024): 3535–46. https://doi.org/10.2298/fil2410535d.

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In this article, we introduce ?-concircular curvature tensor, a new tensor that generalizes the concircular curvature tensor. At first, we produce a few fundamental geometrical properties of ?-concircular curvature tensor and pseudo ?-concircularly symmetric manifolds and provide some inter-esting outcomes. Besides, we investigate ?-concircularly flat spacetimes and establish some significant results about Minkowski spacetime, RW-spacetime, and projective collineation. Moreover, we show that if a ?-concircularly flat spacetime admits a Ricci bi-conformal vector field, then it is either Petrov type N or conformally flat. Moreover, we consider pseudo ? concircularly symmetric spacetime with Codazzi type of Ricci tensor and prove that the spacetime is of Petrov types I, D or O and the spacetime turns into a RW spacetime. Also, we establish that in a pseudo ? concircularly symmetric spacetime with harmonic ?-concircular curvature tensor, the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent. At last, we produce a non-trivial example to validate the existence of4 a (PCS) manifold.
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Book chapters on the topic "Pseudo Ricci symmetric manifold"

1

Willmore, T. J. "Riemannian manifolds." In Riemannian Geometry. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198532538.003.0003.

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Abstract Let M be a differentiable manifold. We say that M carries a pseudo Riemannian metric if there is a differentiable field g = (gm} , m ∈ M, of non-degenerate symmetric bilinear forms gm on the tangent spaces Mm of M. This makes the tangent space into an inner product space. Let Y, Z be differentiable vector fields defined over an open set U of M. By asserting that g is differentiable we mean that the function g( Y, Z) is differentiable. Often we will write < Y, Z> instead of g( Y, Z). If in addition the forms gm are positive definite we call the metric Riemannian. A differentiable manifold with a (pseudo-)Riemannian metric is called a (pseudo-)Riemannian manifold.
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