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Journal articles on the topic 'Pseudo Ricci symmetric manifold'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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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

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2

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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3

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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4

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 fiel

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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 w

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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

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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

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11

Andreeva, T. A., V. V. Balashchenko, D. N. Oskorbin, and E. D. Rodionov. "Conformally Killing Fields on 2-Symmetric Five-Dimensional Lorentzian Manifolds." Izvestiya of Altai State University, no. 1(117) (March 17, 2021): 68–71. http://dx.doi.org/10.14258/izvasu(2021)1-11.

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The papers of many mathematicians are devoted to the study of conformally Killing vector fields. Being a natural generalization of the concept of Killing vector fields, these fields generate a Lie algebra corresponding to the Lie group of conformal transformations of the manifold. Moreover, they generate the class of locally conformally homogeneous (pseudo) Riemannian manifolds studied by V.V. Slavsky and E.D. Rodionov. Ricci solitons, which R. Hamilton first considered, are another important area of research. Ricci solitons are a generalization of Einstein's metrics on (pseudo) Riemannian man

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12

Acet, T. "$\delta$-Almost Ricci soliton on 3-dimensional trans-Sasakian manifold." Carpathian Mathematical Publications 16, no. 2 (2024): 558–64. https://doi.org/10.15330/cmp.16.2.558-564.

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In this paper, we consider $\delta$-almost Ricci soliton on 3-dimensional trans-Sasakian manifold admitting $\eta$-parallel Ricci tensor. We give some conditions for $P\cdot \phi =0$, $P\cdot S=0$, $Q\cdot P=0$. Also, we show that there is almost pseudo symmetric $\delta$-almost Ricci soliton on 3-dimensional trans-Sasakian manifold admitting cyclic Ricci tensor. Finally, we give an example for verifying the obtained results.

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13

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 (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

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14

Yadav, Sunil Kumar, Abdul Haseeb, and Nargis Jamal. "Almost Pseudo Symmetric Kähler Manifolds Admitting Conformal Ricci-Yamabe Metric." International Journal of Analysis and Applications 21 (September 25, 2023): 103. http://dx.doi.org/10.28924/2291-8639-21-2023-103.

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The novelty of the paper is to investigate the nature of conformal Ricci-Yamabe soliton on almost pseudo symmetric, almost pseudo Bochner symmetric, almost pseudo Ricci symmetric and almost pseudo Bochner Ricci symmetric Kähler manifolds. Also, we explore the harmonic aspects of conformal η-Ricci-Yamabe soliton on Kähler spcetime manifolds with a harmonic potential function f and deduce the necessary and sufficient conditions for the 1-form η, which is the g-dual of the vector field ξ on such spacetime to be a solution of Schrödinger-Ricci equation.

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15

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 (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

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16

Ali, Mohabbat, and Mohd Vasiulla. "Almost Pseudo Ricci Symmetric Manifold Admitting Schouten Tensor." Journal of Dynamical Systems and Geometric Theories 19, no. 2 (2021): 217–25. http://dx.doi.org/10.1080/1726037x.2021.2020422.

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17

Tarafdar, Debasish, and U. C. De. "On pseudo symmetric and pseudo Ricci symmetricK-contact manifolds." Periodica Mathematica Hungarica 31, no. 1 (1995): 21–25. http://dx.doi.org/10.1007/bf01876349.

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18

De, Uday Chand, Cengizhan Murathan, and Cihan Ozgur. "PSEUDO SYMMETRIC AND PSEUDO RICCI SYMMETRIC WARPED PRODUCT MANIFOLDS." Communications of the Korean Mathematical Society 25, no. 4 (2010): 615–21. http://dx.doi.org/10.4134/ckms.2010.25.4.615.

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19

Tarafdar, M. "On pseudo-symmetric and pseudo-Ricci-symmetric Sasakian manifolds." Periodica Mathematica Hungarica 22, no. 2 (1991): 125–28. http://dx.doi.org/10.1007/bf02327868.

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20

Baishya, Kanak Kanti, and Ashis Biswas. "Study on generalised pseudo (Ricci) symmetric Sasakian manifold admitting." SERIES III - MATEMATICS, INFORMATICS, PHYSICS 61(12), no. 2 (2020): 233–46. http://dx.doi.org/10.31926/but.mif.2019.61.12.2.4.

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21

Kumar, R. T. Naveen, and Venkat esha. "On Pseudo Ricci-Symmetric N(k) - Contact Metric Manifold." International Journal of Mathematics Trends and Technology 34, no. 2 (2016): 118–21. http://dx.doi.org/10.14445/22315373/ijmtt-v34p520.

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22

Golzarpoor, J., A. A. Hosseinzadeh, and S. Mehrshad. "Some curvature properties on generalized quasi Einstein manifolds." SERIES III - MATEMATICS INFORMATICS PHYSICS 1(63), no. 2 (2022): 53–60. http://dx.doi.org/10.31926/but.mif.2021.1.63.2.5.

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In this article, we first investigate Ricci-pseudosymmetric generalized quasi-Einstein manifolds. Next we study pseudo projectively at generalized quasi Einstein manifolds and pseudo projective Ricci-symmetric generalized quasi Einstein manifolds.

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23

Naik, Shweta, та H. G. Nagaraja. "EQUIVALENT STRUCTURES ON N (κ) MANIFOLD ADMITTING GENERALIZED TANAKA WEBSTER CONNECTION". South East Asian J. of Mathematics and Mathematical Sciences 18, № 03 (2022): 193–206. http://dx.doi.org/10.56827/seajmms.2022.1803.16.

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The main objective of the present paper is to study the equivalence of semi-symmetric and pseudo-symmetric conditions imposing on different curvature tensors in N (κ) manifolds admitting generalized Tanaka Webster ( ˜) connection. Classification is done according as expression of Ricci tensor and scalar curvature with respect to ∇˜. Finally an example is given.

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24

Chaki, M. C., and S. Koley. "On generalized Pseudo Ricci symmetric manifolds." Periodica Mathematica Hungarica 28, no. 2 (1994): 123–29. http://dx.doi.org/10.1007/bf01876902.

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25

Uysal, S. Aynur, and Hülya Bağdatlı Yılmaz. "Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold." Advances in Mathematical Physics 2020 (July 1, 2020): 1–4. http://dx.doi.org/10.1155/2020/6831650.

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The object of the paper is to study some properties of the generalized Einstein tensor GX,Y which is recurrent and birecurrent on pseudo-Ricci symmetric manifolds PRSn. Considering the generalized Einstein tensor GX,Y as birecurrent but not recurrent, we state some theorems on the necessary and sufficient conditions for the birecurrency tensor of GX,Y to be symmetric.

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26

Pahan, Sampa. "On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime". Acta et Commentationes Universitatis Tartuensis de Mathematica 28, № 1 (2024): 75–97. http://dx.doi.org/10.12697/acutm.2024.28.06.

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The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some

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27

CALVARUSO, G., and B. DE LEO. "PSEUDO-SYMMETRIC LORENTZIAN THREE-MANIFOLDS." International Journal of Geometric Methods in Modern Physics 06, no. 07 (2009): 1135–50. http://dx.doi.org/10.1142/s0219887809004132.

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We investigate pseudo-symmetric Lorentzian three-manifolds for the different possible Segre types of the Ricci operator. After determining all three-dimensional pseudo-symmetric Lorentzian algebraic curvature tensors, we classify pseudo-symmetric Lorentzian three-spaces which are either homogeneous, curvature homogeneous up to order 1 or curvature homogeneous, and we also provide some examples which are not curvature homogeneous.

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28

Calvaruso, Giovanni, and Anna Fino. "Four-dimensional pseudo-Riemannian homogeneous Ricci solitons." International Journal of Geometric Methods in Modern Physics 12, no. 05 (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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29

Gupta, P. "Index of pseudo-projectively-symmetric semi-Riemannian manifolds." Carpathian Mathematical Publications 7, no. 1 (2015): 57–65. http://dx.doi.org/10.15330/cmp.7.1.57-65.

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The index of $\widetilde{\nabla}$-pseudo-projectively symmetric and in particular for $\widetilde{\nabla}$-projectively symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is Ricci symmetric metric connection, are discussed.

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30

Mantica, Carlo Alberto, and Luca Guido Molinari. "On conformally recurrent manifolds of dimension greater than 4." International Journal of Geometric Methods in Modern Physics 13, no. 05 (2016): 1650053. http://dx.doi.org/10.1142/s0219887816500535.

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Conformally recurrent pseudo-Riemannian manifolds of dimension [Formula: see text] are investigated. The Weyl tensor is represented as a Kulkarni–Nomizu product. If the square of the Weyl tensor is non-zero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the traceless part of the Ricci tensor is obtained, up to a scalar function. The Ricci tensor has at most two distinct eigenvalues, and the recurrence vector is an eigenvector. Lorentzian conformally recurrent manifolds are then considered. If

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31

Li, Yanlin, Aydin Gezer, and Erkan Karakaş. "Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection." AIMS Mathematics 8, no. 8 (2023): 17335–53. http://dx.doi.org/10.3934/math.2023886.

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<abstract><p>Let $ (M, g) $ be an $ n $-dimensional (pseudo-)Riemannian manifold and $ TM $ be its tangent bundle $ TM $ equipped with the complete lift metric $ ^{C}g $. First, we define a Ricci quarter-symmetric metric connection $ \overline{\nabla } $ on the tangent bundle $ TM $ equipped with the complete lift metric $ ^{C}g $. Second, we compute all forms of the curvature tensors of $ \overline{\nabla } $ and study their properties. We also define the mean connection of $ \overline{\nabla } $. Ricci and gradient Ricci solitons are important topics studied extensively lately. N

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32

De, U. C., and Dibakar Dey. "Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions." Acta et Commentationes Universitatis Tartuensis de Mathematica 23, no. 1 (2019): 13–24. http://dx.doi.org/10.12697/acutm.2019.23.02.

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The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (k; μ)-, (k; μ)′-, and generalized (k; μ)-nullity distributions. We also characterize (k; μ)-almost Kenmotsu manifolds satisfying the condition R ⋅ S = LꜱQ(g; S2).

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33

Devi, S. Sunitha, K. L. Sai Prasad, and G. V. S. R. Deekshitulu. "On Ricci pseudo-symmetric para-Kenmotsu manifolds." New Trends in Mathematical Science 1, no. 6 (2018): 99–105. http://dx.doi.org/10.20852/ntmsci.2018.250.

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34

Chaki, M. C., and M. Tarafdar. "On conformally flat pseudo-Ricci symmetric manifolds." Periodica Mathematica Hungarica 19, no. 3 (1988): 209–15. http://dx.doi.org/10.1007/bf01850289.

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35

ÖZTÜRK, Hakan. "The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures". Afyon Kocatepe University Journal of Sciences and Engineering 22, № 6 (2022): 1314–22. http://dx.doi.org/10.35414/akufemubid.1169777.

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This paper aims to study some semi-symmetric and curvature tensor conditions on α-Kenmotsu pseudo-metric manifolds. Some conditions of semi-symmetric, locally symmetric, and the Ricci semi-symmetric are considered on such manifolds. Also, the relationships between the M-projective curvature tensor and conformal curvature tensor, concircularly curvature tensor, and conharmonic curvature tensor are investigated. Finally, an example of α-Kenmotsu pseudo-metric structure is given.

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36

Shenawy, Sameh, Uday Chand De, Nasser Bin Turki, and Naeem Ahmad Pundeer. "Projective Collineations in Warped Product Manifolds and (PRS)n Manifolds." Symmetry 15, no. 9 (2023): 1644. http://dx.doi.org/10.3390/sym15091644.

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The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ=ζ1+ζ2 are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse’s problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci sym

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Mofarreh, Fatemah, Krishnendu De та Uday De. "Characterizations of a spacetime admitting ψ-conformal curvature tensor". Filomat 37, № 30 (2023): 10265–74. http://dx.doi.org/10.2298/fil2330265m.

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In this paper, we introduce ?-conformal curvature tensor, a new tensor that generalizes the conformal curvature tensor. At first, we deduce a few fundamental geometrical properties of ?-conformal curvature tensor and pseudo ?-conharmonically symmetric manifolds and produce some interesting outcomes. Moreover, we study ?-conformally flat perfect fluid spacetimes. As a consequence, we establish a number of significant theorems about Minkowski spacetime, GRW-spacetime, projective collineation. Moreover, we show that if a?-conformally flat spacetime admits a Ricci bi-conformal vector field, then i

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38

Mantica, Carlo Alberto, and Young Jin Suh. "On weakly conformally symmetric pseudo-Riemannian manifolds." Reviews in Mathematical Physics 29, no. 03 (2017): 1750007. http://dx.doi.org/10.1142/s0129055x17500076.

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In this paper, we study the properties of weakly conformally symmetric pseudo- Riemannian manifolds focusing particularly on the [Formula: see text]-dimensional Lorentzian case. First, we provide a new proof of an important result found in literature; then several new others are stated. We provide a decomposition for the conformal curvature tensor in [Formula: see text]. Moreover, some important identities involving two particular covectors are stated; for example, it is proven that under certain conditions the Ricci tensor and other tensors are Weyl compatible. Topological properties involvin

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39

Li, Yanlin, Aydin Gezer, and Erkan Karakas. "Exploring Conformal Soliton Structures in Tangent Bundles with Ricci-Quarter Symmetric Metric Connections." Mathematics 12, no. 13 (2024): 2101. http://dx.doi.org/10.3390/math12132101.

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In this study, we investigate the tangent bundle TM of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection ∇˜. Our primary goal is to establish the necessary and sufficient conditions for TM to exhibit characteristics of various solitons, specifically conformal Yamabe solitons, gradient conformal Yamabe solitons, conformal Ricci solitons, and gradient conformal Ricci solitons. We determine that for TM to be a conformal Yamabe soliton, the potential vector field must satisfy certain conditions when lifted vertically, horizontally, or complet

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40

Duggal, K. L. "A New Class of Contact Pseudo Framed Manifolds with Applications." International Journal of Mathematics and Mathematical Sciences 2021 (August 26, 2021): 1–9. http://dx.doi.org/10.1155/2021/6141587.

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In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M , g , f , λ , ξ by a real tensor field f of type 1,1 , a real function λ such that f 3 = λ 2 f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Blair proved that the vector field ξ of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general, ξ of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations sym

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41

Diallo, Abdoul Salam, and Punam Gupta. "Four-Dimensional Semi-Riemannian Szabó Manifolds." Journal of Mathematics 2020 (December 31, 2020): 1–5. http://dx.doi.org/10.1155/2020/6663361.

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In this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice versa. We prove that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the necessary and sufficient condition for the affine Szabó surface to be recurrent. We prove that, for an affine Szabó recurrent surface, the recurrence covector of a recurrence tensor is not locally a gradient.

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42

Shaikh, A. A., C. Özgür, and S. K. Jana. "On generalized pseudo Ricci symmetric manifolds admitting semi-symmetric metric connection." Proceedings of the Estonian Academy of Sciences 59, no. 3 (2010): 207. http://dx.doi.org/10.3176/proc.2010.3.03.

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43

DE, UDAY CHAND, and PRAJJWAL PAL. "On some classes of almost pseudo Ricci symmetric manifolds." Publicationes Mathematicae Debrecen 83, no. 1-2 (2013): 207–25. http://dx.doi.org/10.5486/pmd.2013.5675.

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44

GUPTA, Brijesh, and B. B. Chaturvedi. "On Ricci pseudo-symmetric super quasi-Einstein Hermitian manifolds." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 69, no. 1 (2020): 172–82. http://dx.doi.org/10.31801/cfsuasmas.432858.

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Blaga, Adara M. "Differentiable Manifolds and Geometric Structures." Mathematics 13, no. 7 (2025): 1082. https://doi.org/10.3390/math13071082.

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This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in different areas of differential geometry, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as Golden space forms, Sasakian space forms; diffeological and affine connection spaces; Weingarten and Delaunay surfaces;

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Baḡdatlı Yılmaz, Hülya, та S. Aynur Uysal. "Compatibility of φ(Ric)-vector fields on almost pseudo-Ricci symmetric manifolds". International Journal of Geometric Methods in Modern Physics 18, № 08 (2021): 2150128. http://dx.doi.org/10.1142/s0219887821501280.

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The object of the paper is to study the compatibility of [Formula: see text]-vector fields on almost pseudo-Ricci symmetric manifolds, briefly [Formula: see text]. First, we show the existence of an [Formula: see text] whose basic vector field [Formula: see text] is a [Formula: see text]-vector field by constructing a non-trivial example. Then, we investigate the properties of the Riemann and Weyl compatibility of [Formula: see text] under certain conditions. We consider an [Formula: see text] space-time whose basic vector fields [Formula: see text] and [Formula: see text] is [Formula: see tex

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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 (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 investiga

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Pavlova, A. A., O. P. Khromova, E. D. Rodionov, and D. V. Vylegzhanin. "On the Symmetric Einstein Equation for Three-Dimensional Lie Groups with Left-Invariant Riemannian Metric and Semi-Symmetric Connection." Izvestiya of Altai State University, no. 4(126) (September 9, 2022): 140–43. http://dx.doi.org/10.14258/izvasu(2022)4-21.

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Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most studied in the homogeneous Riemannian case. In this direction, the most famous ones are the results of works by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov and other mathematicians. At the same time, the question of studying Einstein manifolds has been little studied for the case of an arbitrary metric connection. This is primarily due to the fact that the Ricci tensor of

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Fuster, Andrea, Sjors Heefer, Christian Pfeifer, and Nicoleta Voicu. "On the Non Metrizability of Berwald Finsler Spacetimes." Universe 6, no. 5 (2020): 64. http://dx.doi.org/10.3390/universe6050064.

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We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern–Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi–Civita connection of some Riemannian metric. We show for the first time that this result does not extend to general Finsler spacetimes. More precisely, we find a large class of Berwal

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De, Uday Chand, and Avik De. "On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity." Czechoslovak Mathematical Journal 62, no. 4 (2012): 1055–72. http://dx.doi.org/10.1007/s10587-012-0063-0.

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