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Journal articles on the topic 'Curvature tensor U_jkh^i'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Abdalstar, A. Saleem Alaa A. Abdallah and Ammar Z. Hussein. "Study on Generalized U_(|l|m) - Birecurrent Finsler Space." International Journal of Advanced Scientific and Technical Research 15, no. 2 (2025): 15–27. https://doi.org/10.5281/zenodo.15369382.

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<strong>Abstract: </strong>In this paper, we got the necessary and sufficient condition for some tensors to be generalized birecurrent. The relationship between the curvature tensors have been studied. Also, some results in the projection on indicatrix with respect to Cartan connection have been discussed.  

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2

Chandru, K., and S. K. Narasimhamurthy. "The Study of Decomposition of Curvature Tensor Field in a Kaehlerian Recurrent Space of First Order." Journal of the Tensor Society 3, no. 00 (2009): 11–18. http://dx.doi.org/10.56424/jts.v3i01.9967.

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Takano [2] have studied decomposition of curvature tensor in a recurrent space. Sinha and Singh [3] have been studied and defined decomposition of recurrent curvature tensor field in a Finsler space. Singh and Negi studied decomposition of recurrent curvature tensor field in a Kaehlerian space. Negi and Rawat [6] have studied decomposition of recurrent curvature tensor field in a Kaehlerian space. Rawat and Silswal [11] studied and defined decomposition of recurrent curvature tensor fields in a Tachibana space. In the present paper, we have studied the decomposition of curvature tensor fields

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3

Chandru, K., and S. K. Narasimhamurthy. "The Study of Decomposition of Curvature Tensor Field in a Kaehlerian Recurrent Space of First Order." Journal of the Tensor Society 3, no. 01 (2009): 11–18. http://dx.doi.org/10.56424/jts.v3i00.9967.

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Takano [2] have studied decomposition of curvature tensor in a recurrent space. Sinha and Singh [3] have been studied and defined decomposition of recurrent curvature tensor field in a Finsler space. Singh and Negi studied decomposition of recurrent curvature tensor field in a Kaehlerian space. Negi and Rawat [6] have studied decomposition of recurrent curvature tensor field in a Kaehlerian space. Rawat and Silswal [11] studied and defined decomposition of recurrent curvature tensor fields in a Tachibana space. In the present paper, we have studied the decomposition of curvature tensor fields

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4

Baishya, Kanak Kanti, and Partha Roy Chowdhury. "Deszcz Pseudo Symmetry Type LP-Sasakian Manifolds." Annals of West University of Timisoara - Mathematics and Computer Science 54, no. 1 (2016): 35–53. http://dx.doi.org/10.1515/awutm-2016-0003.

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Abstract Recently the present authors introduced the notion of generalized quasi-conformal curvature tensor which bridges Conformal curvature tensor, Concircular curvature tensor, Projective curvature tensor and Conharmonic curvature tensor. This paper attempts to charectrize LP-Sasakian manifolds with ω(X, Y) · 𝒲 = L{(X ∧ɡ Y) · 𝒲}. On the basis of this curvature conditions and by taking into account, the permutation of different curvature tensors we obtained and tabled the nature of the Ricci tensor for the respective pseudo symmetry type LP-Sasakian manifolds.

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5

Acet, Bilal Eftal, Erol Kılıç, and Selcen Yüksel Perktaş. "Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–24. http://dx.doi.org/10.1155/2012/395462.

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We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is anη-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor,W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constan

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6

Rawat, K. S., and Sandeep Chauhan. "Study on Einstein-Sasakian Decomposable Recurrent Space of First Order." Journal of the Tensor Society 12, no. 01 (2009): 85–92. http://dx.doi.org/10.56424/jts.v12i01.10589.

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Takano [2] have studied decomposition of curvature tensor in a recurrent space. Sinha and Singh [3] have been studied and defined decomposition of recurrent curvature tensor field in a Finsler space. Singh and Negi studied decomposition of recurrent curvature tensor field in a K¨aehlerian space. Negi and Rawat [6] have studied decomposition of recurrent curvature tensor field in K¨aehlerian space. Rawat and Silswal [11] studied and defined decomposition of recurrent curvature tensor fields in a Tachibana space. Rawat and Kunwar Singh [12] studied the decomposition of curvature tensor field in

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7

Bhattacharyya, A., та C. Patra. "Some Curvature Tensors of a Semi Symmetric Metric φ−Connection in an LSP-Sasakian Manifold". Journal of the Tensor Society 5, № 01 (2007): 67–75. http://dx.doi.org/10.56424/jts.v5i01.10440.

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The purpose of this paper is to investigate the conditions for the pseudo- projective curvature tensor and quasi-conformal curvature tensor of a semi- symmetric metric Á-connection to be the pseudo-projective curvature tensor and quasi-conformal curvature tensor of a Levi-Civita connection on LSP-Sasakian manifold. Also we shall discuss the behavior of conharmonic curvature ten- sor and Tachibana concircular curvature tensor with respect to semi-symmetric metric Á-connection on LSP-Sasakian manifold.

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8

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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9

Güler, Sinem, and Sezgin Demirbağ. "On some classes of generalized quasi Einstein manifolds." Filomat 29, no. 3 (2015): 443–56. http://dx.doi.org/10.2298/fil1503443g.

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In the present paper, we investigate generalized quasi Einstein manifolds satisfying some special curvature conditions R?S = 0,R?S = LSQ(g,S), C?S = 0,?C?S = 0,?W?S = 0 and W2?S = 0 where R, S, C,?C,?W and W2 respectively denote the Riemannian curvature tensor, Ricci tensor, conformal curvature tensor, concircular curvature tensor, quasi conformal curvature tensor and W2-curvature tensor. Later, we find some sufficient conditions for a generalized quasi Einstein manifold to be a quasi Einstein manifold and we show the existence of a nearly quasi Einstein manifolds, by constructing a non trivia

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10

Rawat, K. S., and Sandeep Chauhan. "Study on Einstein-K ̈aehlerian Decomposable Recurrent Space of First Order." Journal of the Tensor Society 9, no. 01 (2007): 45–51. http://dx.doi.org/10.56424/jts.v9i01.10567.

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Takano [2] have studied decomposition of curvature tensor in a recurrent space. Sinha and Singh [3] have been studied and defined decomposition of recurrent curvature tensor field in a Finsler space. Singh and Negi studied decomposition of recurrent curvature tensor field in a K¨aehlerian space. Negi and Rawat [6] have studied decomposition of recurrent curvature tensor field in K¨aehlerian space. Rawat and Silswal [11] studied and defined decomposition of recurrent curvature tensor fields in a Tachibana space. Further, Rawat and Kunwar Singh [12] studied the decomposition of curvature tensor

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11

Shaikh, Absos Ali, and Haradhan Kundu. "Some curvature restricted geometric structures for projective curvature tensors." International Journal of Geometric Methods in Modern Physics 15, no. 09 (2018): 1850157. http://dx.doi.org/10.1142/s0219887818501578.

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The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds. It possesses different geometric properties than other generalized curvature tensors. The main object of the present paper is to study some semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor. The reduced pseudosymmetric type structures for various Walker type conditions are deduced and the existence of Venzi space is ensured. It is shown that the geometric structures formed by imposing projective operator o

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12

Vasiulla, Mohd, Quddus Khan, and Mohabbat Ali. "ON SOME CLASSES OF MIXED GENERALIZED QUASI-EINSTEIN MANIFOLDS." Jnanabha 52, no. 01 (2022): 182–88. http://dx.doi.org/10.58250/jnanabha.2022.52124.

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In this paper we study mixed generalized quasi-Einstein manifold satisfying some curvature conditions like K.Ric = 0, C.Ric = 0, N.Ric = 0, where K, Ric, C and N denote the Reimannian curvature tensor, Ricci tensor, conformal curvature tensor and concircular curvature tensor and obtain some interesting and fruitful results on it.

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13

Adel M. Al-Qashbari and Saeedah M. Baleedi. "A study of the concircular curvature tensor and its interactions with other tensors under the Lie derivative in \(GBK- 5RF_n\)." University of Aden Journal of Natural and Applied Sciences 28, no. 2 (2025): 89–96. https://doi.org/10.47372/uajnas.2024.n2.a08.

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This research paper delves into a comprehensive analysis of the concircular curvature tensor and its intricate relationships with other tensors under the Lie derivative. The concircular curvature tensor, a fundamental geometric invariant, plays a pivotal role in characterizing the local geometry of Riemannian manifolds. By employing the powerful tool of the Lie derivative, we explore how the concircular curvature tensor transforms under infinitesimal transformations of the underlying manifold. Our study uncovers novel connections between the concircular curvature tensor and other significant t

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14

Khan, Mohammad. "Liftings from a para-Sasakian manifold to its tangent bundles." Filomat 37, no. 20 (2023): 6727–40. http://dx.doi.org/10.2298/fil2320727k.

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The purpose of the present paper is to study the liftings of a quarter symmetric non-metric connection from a para-Sasakian manifold to its tangent bundles. By liftings, some results of the curvature tensor, projective curvature tensor, concircular curvature tensor and conformal curvature tensor wrt a quarter symmetric non-metric connection in a P-Sasakian manifold to its tangent bundles are obtained.

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15

Matsumoto, Koji. "A new curvaturelike tensor field in an almost contact Riemannian manifold II." Publications de l'Institut Math?matique (Belgrade) 103, no. 117 (2018): 113–28. http://dx.doi.org/10.2298/pim1817113m.

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In the last paper, we introduced a new curvaturlike tensor field in an almost contact Riemannian manifold and we showed some geometrical properties of this tensor field in a Kenmotsu and a Sasakian manifold. In this paper, we define another new curvaturelike tensor field, named (CHR)3-curvature tensor in an almost contact Riemannian manifold which is called a contact holomorphic Riemannian curvature tensor of the second type. Then, using this tensor, we mainly research (CHR)3-curvature tensor in a Sasakian manifold. Then we define the notion of the flatness of a (CHR)3-curvature tensor and we

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16

Al-Qashbari, Adel M., and Saeedah M. Baleedi. "ON THE LIE DERIVATIVE OF CURVATURE TENSORS AND THEIR RELATIONS IN \(GBK- 5RF_n\)." Electronic Journal of University of Aden for Basic and Applied Sciences 5, no. 4 (2024): 464–68. https://doi.org/10.47372/ejua-ba.2024.4.403.

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This paper investigates the behavior of curvature tensors under the Lie derivative. We derive novel relations between various curvature tensors, such as the Riemann curvature tensor, Ricci tensor, and scalar curvature, when subjected to the Lie derivative. Our results provide a deeper understanding of the geometric properties of manifolds and have potential applications in fields such as general relativity and differential geometry. Also, we build upon the definitions for the conformal and conharmonice curvature tensor in generaralized fifth recurrent Finsler space \(GBK-5RF_n\). We study the

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17

Jain, Swati, M. K. Pandey, and A. Goyal. "ON PARA-KENMOTSU MANIFOLDS ADMITTING ZAMKOVOY CONNECTION." jnanabha 54, no. 02 (2024): 158–70. https://doi.org/10.58250/jnanabha.2024.54215.

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The goal of this paper is to study a PK-manifold (briefly, PK-manifold) that admits a Zamkovoy connection. We use a new (0, 2) type symmetric tensor Z to derive a new tensor field from the Mprojective curvature tensor (briefly, MP-curvature tensor). We call this new tensor field as generalised M-projective curvature tensor (briefly, GMP-curvature tensor). Further, we prove that a generalized M-projectively semi-symmetric PK-manifold turns out to be an Einstein manifold. Among others, it has been shown that the condition of generalized M-projectively φ-symmetry on PK-manifold admitting a Zamkov

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18

Al-Qashbari, Adel Mohammed Ali, and Abdullah Saeed Abdullah Saeed. "Decomposition of Curvatur tensor filed \(R_jkh^i \) recurrent spaces of first and second order." University of Aden Journal of Natural and Applied Sciences 27, no. 2 (2023): 281–89. http://dx.doi.org/10.47372/uajnas.2023.n2.a09.

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Finsler geometry has many uses in relative physics and many of mathematicians contributed in this study and improved it. Takano [26] has studied the decomposition of curvature tensor in a recurrent space. Sinha and Singh [25] have studied and deﬁned the decomposition of recurrent curvature tensor ﬁeld in a Finsler space. Negi and Rawat [11] and [12] have studied decomposition of recurrent curvature tensor ﬁelds in K¨aehlerian space. Rawat and Silswal [19] studied and deﬁned the decomposition of recurrent curvature tensor ﬁelds in a Tachibana space. Rawat and Singh [21] studied the decompositio

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19

Takano, Kazuhiko. "K"ahlerian submersions with vanishing Bochner curvature tensor." Tamkang Journal of Mathematics 31, no. 1 (2000): 21–32. http://dx.doi.org/10.5556/j.tkjm.31.2000.411.

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In this paper, we discuss the K"ahlerian submersion with vanishing Bochner curvature tensor and prove that the Bochner curvature tensor of the base space vanishes. Also, we seek a sufficient condition with respect to the length of the Ricci tensor of each fiber that the Bochner curvature tensor of each fiber vanishes.

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20

S. R. Ashoka, C. S. Bagewadi та Gurupadavva Ingalahalli. "Curvature tensor of almost C(λ) manifolds". Malaya Journal of Matematik 2, № 01 (2014): 10–15. http://dx.doi.org/10.26637/mjm201/002.

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The present paper deals with certain characterization of curvature conditions on Pseudo-projective and Quasi-conformal curvature tensor on almost $C(\lambda)$ manifolds. The main object of the paper is to study the flatness of the Pseudo-projective, Quasi-conformal curvature tensor, $\xi$-Pseudo-projective, $\xi$-Quasi-conformal curvature tensor on almost $C(\lambda)$ manifolds.

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21

Prasad, Rajendra, та Vinay Kumar. "Conformal η-Ricci soliton in Lorentzian para Kenmotsu manifolds". Gulf Journal of Mathematics 14, № 2 (2023): 54–67. http://dx.doi.org/10.56947/gjom.v14i2.931.

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The objective of the present paper is to study conformal η-Ricci soliton on Lorentzian Para-Kenmotsu manifolds with some curvature conditions. We study Concircular curvature tensor, Quasi conformal curvature tensor, Codazi type of Ricci tensor and cyclic parallel Ricci tensor in Lorentzian Para-Kenmotsu manifolds. At last we give examples of such manifolds.

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22

Obaje, VIivian Onechojo. "A comparative study of the Schwarzschild metric tensor and the Howusu metric tensor using the radial distance parameter as a measuring index." Journal of Physics: Theories and Applications 7, no. 2 (2023): 214. http://dx.doi.org/10.20961/jphystheor-appl.v7i2.77212.

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<p align="justify">The Einstein Curvature Tensor using Schwarzschild Metric Tensor and the Howusu Metric Tensor were investigated. The Einstein Curvature Tensor derived from the Howusu Metric Tensor were compared to the Einstein Curvature Tensor derived from the Schwarzschild Metric Tensor. Results of the analysis indicated that the behavior of the Howusu were, to a large extent behaved differently from that of the Schwarzschild in the limit as the radial distance .Similar results were also obtained in the limit as .</p>

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23

Li, Benling, and Zhongmin Shen. "Ricci Curvature Tensor and Non-Riemannian Quantities." Canadian Mathematical Bulletin 58, no. 3 (2015): 530–37. http://dx.doi.org/10.4153/cmb-2014-063-4.

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AbstractThere are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. Using this Ricci curvature tensor, we shall have a better understanding of these non-Riemannian quantities.

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24

Negi, U. S., Preeti Chauhan, and Sulochana. "Decomposition of Riemannian Recurrent Curvature Tensor Manifolds of First Order." Journal of Nepal Mathematical Society 5, no. 2 (2022): 65–71. http://dx.doi.org/10.3126/jnms.v5i2.50082.

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Takano [6] premeditated decomposition of curvature tensor in a recurrent Riemannian space. After that, Negi and Bisht [3] defined and deliberated decomposition of recurrent curvature tensor fields in a Kaehlerian manifolds of first order. We have calculated the decomposition of Riemannian recurrent curvature tensor manifolds of first order and some theorems established using the decomposition tensor field.

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25

Obaje, V. O., K. O. Emeje, and I. Ochala. "The Relationship between Howusu and Schwarzschild Metric Tensors in Deriving Ricci Curvature Tensor for All Gravitational Fields in Nature." RESEARCH JOURNAL OF PURE SCIENCE AND TECHNOLOGY 5, no. 2 (2022): 13–18. http://dx.doi.org/10.56201/rjpst.v5.no2.2022.pg13.18.

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The Howusu metric tensor which was said to describe the gravitational field for all gravitational fields in nature was used to derive the Ricci Curvature Tensor R_μν. Results obtained were compared with the Ricci Curvature Tensor R_μν derived from the well-known Schwarzschild metric tensor. It was found that, at r→0, the Ricci Curvature Tensor for both metric tensors were different but behaved the same, as r→∞,

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26

Rawat, K. S., and Nitin Uniyal. "Study on Kaehlerian Recurrent and Symmetric Spaces of Second Order." Journal of the Tensor Society 4, no. 01 (2007): 69–76. http://dx.doi.org/10.56424/jts.v4i01.10422.

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Tachibana (1967), Singh (1971) studied and defined the Bochner curvature tensor and Kaehlerian spaces with recurrent Bochner curvature tensor. Further , Negi and Rawat (1994), (1997) studied some bi-recurrence and bi-symmetric properties in a Kaehlerian space and Kaehlerian spaces with recurrent and symmetric Bochner curvature tensor. In the present paper, we have studied Kaehlerian recurrent and symmetric spaces of second order by taking different curvature tensor and relations between them. Also several theorems have been established therein.

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27

Al-Qashbari, Adel Mohammed Ali. "A Study of the M-Projective Curvature Tensor in Generalized Recurrent and Birecurrent Finsler Spaces." Journal of Science and Technology 30, no. 6 (2025): 87–86. https://doi.org/10.20428/jst.v30i6.2917.

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This paper aims to examine the properties of the M-projective curvature tensor in the context of generalized Finsler spaces, specifically within the framework of a -space. The study begins with the derivation of the M-projective curvature tensor, which is expressed as the sum of the standard M-projective curvature tensor and additional terms involving the Ricci tensor and scalar curvature. Through covariant differentiation, the behavior of this tensor under certain conditions is analyzed, leading to a set of conditions necessary for the space to exhibit generalized recurrent Finsler properties

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28

Adel Mohammed Ali Al-Qashbari and Fahmi Ahmed Mothana AL-ssallal. "Generalized Bi-Recurrent Structures in \(G^{2nd} C_{|h} -RF_n\) Spaces via the Weyl Conformal Curvature Tensor." Journal of the Faculties of Education - University of Aden 19, no. 1 (2025): 320–30. https://doi.org/10.47372/jef.(2025)19.1.135.

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In this paper, we investigate the properties of the Weyl conformal curvature tensor \(C_{jkh}^i\) in the context of n=4 Riemannian and Finslerian spaces, with a particular focus on generalized recurrent and birecurrent structures. We derive several equivalent forms of the conformal curvature tensor under various covariant derivatives, revealing deep interrelations between curvature tensors, Ricci tensors, scalar curvature, and their derivatives. By transvecting the conformal curvature expressions with vectors such as yi, yk, and tensors such as gij we deduce necessary and sufficient conditions

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29

Liu, Liulin, Xiaoling Zhang, and Lili Zhao. "Kropina Metrics with Isotropic Scalar Curvature." Axioms 12, no. 7 (2023): 611. http://dx.doi.org/10.3390/axioms12070611.

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In this paper, we study Kropina metrics with isotropic scalar curvature. First, we obtain the expressions of Ricci curvature tensor and scalar curvature. Then, we characterize the Kropina metrics with isotropic scalar curvature on by tensor analysis.

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30

Decu, S., M. Petrovic-Torgasev, A. Sebekovic, and L. Verstraelen. "On the intrinsic Deszcz symmetries and the extrinsic Chen character of Wintgen ideal submanifolds." Tamkang Journal of Mathematics 41, no. 2 (2010): 109–16. http://dx.doi.org/10.5556/j.tkjm.41.2010.662.

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In this paper it is shown that all Wintgen ideal submanifolds in ambient real space forms are Chen submanifolds. It is also shown that the Wintgen ideal submanifolds of dimension $ >3 $ in real space forms do intrinsically enjoy some curvature symmetries in the sense of Deszcz of their Riemann--Christoffel curvature tensor, of their Ricci curvature tensor and of their Weyl conformal curvature tensor.

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Chongshan, Luo. "On concircular transformations in Riemannian spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 2 (1986): 218–25. http://dx.doi.org/10.1017/s1446788700027191.

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AbstractThis paper introduces a tensor that contains the Riemannian curvature tensor and the conformal curvature tensor as special examples in the Riemannian space (Mn, g), and by using this tensor we define C-semi-symmetric space. In this paper, we have the following main result: if there is a non-trivial concircular transformation between two C-semi-symmetric spaces, then both spaces are of quasi-constant curvature.

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Al-Qashbari, Adel Mohammed Ali. "On generalized for curvature Tensor \(P_{jkh}^i\) of second order in Finsler space." University of Aden Journal of Natural and Applied Sciences 24, no. 1 (2022): 171–76. http://dx.doi.org/10.47372/uajnas.2020.n1.a14.

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In this present paper, we introduced a Finsler space \(F_n\) which Cartan’s second curvature tensor \(P_{jkh}^i\) satisfies the generalized birecurrence property with respect to Berwald’s connection parameters \(G_{kh}^i\) which given by the condition\(B_n B_m P_{jkh}^i = a_{mn} P_{jkh}^i + b_{mn} ( δ_h^i g_{jk} - δ_k^i g_jh ) - 2 μ_m B_r (δ_h^i C_{jkn} - δ_k^i C_{jhn} ) y^r ,P_jkh^i≠0,\)where \(B_n B_m\) is Berwald’ scovariant differential of second order with respect to \(x^m\) and \(x^n\), successively, \(μ_m\) is non-zero covariant vector field, \(a_{mn}\) and \(b_{mn}\) are non-zero recur

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Fu, Jixiang, Weimin Sheng, and Lixia Yuan. "Prescribed k-Curvature Problems on Complete Noncompact Riemannian Manifolds." International Mathematics Research Notices 2020, no. 23 (2018): 9559–92. http://dx.doi.org/10.1093/imrn/rny262.

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Abstract To study the prescribed $k$-curvature problem of 2nd-order symmetric curvature tensors on complete noncompact Riemannian manifolds, we consider a class of fully nonlinear elliptic partial differential equations. It is proved that on a Riemannian manifold with negative sectional curvature and Ricci curvature bounded from below, the equation is solvable provided that all the eigenvalues of the tensor are negative. The result is applicable to the prescribed $k$-curvature problems of modified Schouten tensor and Bakry–Émery Ricci tensor.

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BROZOS-VÁZQUEZ, M., P. GILKEY, and E. MERINO. "GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS." International Journal of Geometric Methods in Modern Physics 07, no. 03 (2010): 505–15. http://dx.doi.org/10.1142/s0219887810004403.

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We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a para-Kaehler manifold of constant scalar curvature.

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35

Kumar, Rajesh, Laltluangkima Chawngthu, Oğuzhan Bahadır, and Meraj Ali Khan. "Geometry of LP-Sasakian Manifolds Admitting a General Connection." Mathematics 13, no. 6 (2025): 902. https://doi.org/10.3390/math13060902.

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This paper concerns certain properties of projective curvature tensor, conharmonic curvature tensor, quasi-conharmonic curvature tensor, and Ricci semi-symmetric conditions with respect to the general connection in an LP-Sasakian manifold. We also provide the applications of LP-Sasakian manifolds admitting general connections in the context of the general theory of relativity.

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36

ZHANG, JIAN-FENG. "The length of curvature tensor for Riemannian manifold with parallel Ricci curvature tensor." Publicationes Mathematicae Debrecen 78, no. 3-4 (2011): 505–12. http://dx.doi.org/10.5486/pmd.2011.4447.

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37

Shenawy, Sameh, and Bülent Ünal. "The W2-curvature tensor on warped product manifolds and applications." International Journal of Geometric Methods in Modern Physics 13, no. 07 (2016): 1650099. http://dx.doi.org/10.1142/s0219887816500997.

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The purpose of this paper is to study the [Formula: see text]-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson–Walker and standard static space-times. Some different expressions of the [Formula: see text]-curvature tensor on a warped product manifold in terms of its relation with [Formula: see text]-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate [Formula: see text]-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a [Formula: see text]-

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Alaa, A. Abdallah, M. Al-Qashbari Adel, and M. Baleedi Saeedah. "Berwald Covariant Derivative and Lie Derivative of Conharmonic Curvature Tensors in Generalized Fifth Recurrent Finsler Space." GPH - International Journal of Mathematics 8, no. 01 (2025): 24–32. https://doi.org/10.5281/zenodo.14836508.

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This paper builds upon new define for the conharmonice curvature tensor in generaralized fifth recurrent Finsler space that Cartan’s fourth curvature tensor  in sense of Berwald <em>-</em>  via Lie derivative. We define a new conharmonic curvature tensor and explore its relationships with other established curvature tensors. Through various mathematical operations, including the Berwald covariant derivative and the Lie derivative, we derive new expressions for the conharmonic tensor and its interactions with other curvature tensors. The main results include the commutativity of

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39

Ali A. Shihab and Dhabiaʼa M. Ali. "GENERELIZED CONHARMONIC CURVATURE TENSOR OF NEARLY KAHLER MANIFOLD." Tikrit Journal of Pure Science 23, no. 8 (2018): 105–9. http://dx.doi.org/10.25130/tjps.v23i8.551.

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In this paper we study the relationship between tensor algebraic curvature tensor, and General conharmonic curvature tensor of Nearly Kahler manifold, i. e. it has a classical symmetry properties of the Riemann carvatur tensor. Relpenishing generalized Riemannian structur of certain classes of almost Hermitian manifold allows an additional symmetry properties of this tensor.

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40

Alhamadi, Khaled M., Fahmi Yaseen Qasem, and Meqdad Ahmed Ali. "Different types of decomposition for certain tensors in \(K^h-BR-F_n\) and \(K^h-BR\)-affinely connected space." University of Aden Journal of Natural and Applied Sciences 20, no. 2 (2016): 355–63. http://dx.doi.org/10.47372/uajnas.2016.n2.a10.

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In this paper we defined \(K^h\)-birecurrent space which is characterized by the condition\(K_jkh|m|l^i=a_lm K_jkh^i\) , \(K_jkh^i≠0\), also we introduced some decompositions of Cartan's fourth and third curvature tensor and Berwald curvature tensor and its torsion tensor. The aim of this paper is devoted to the discussion of decomposition for different tensors in \(K^h\)-birecurrent space and \(K^h\)-birecurrent affinely connected space and the decomposition of curvature tensor Cartan's fourth and third in \(K^h\)-birecurrent space, also the decomposition of curvature tensor of Berwald in \(K

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41

Brooks, Thomas G. "Nonnegative curvature and conullity of the curvature tensor." Annals of Global Analysis and Geometry 56, no. 3 (2019): 555–66. http://dx.doi.org/10.1007/s10455-019-09678-5.

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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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Elsharkawy, Ayman, Hoda Elsayied, Abdelrhman Tawfiq, and Fatimah Alghamdi. "Geometric analysis of the pseudo-projective curvature tensor in doubly and twisted warped product manifolds." AIMS Mathematics 10, no. 1 (2025): 56–71. https://doi.org/10.3934/math.2025004.

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<p>This study investigates the pseudo-projective curvature tensor within the framework of doubly and twisted warped product manifolds. It offers significant insights into the interaction between the pseudo-projective curvature tensor and both the base and fiber manifolds. The research highlights key geometric characteristics of the base and fiber manifolds as influenced by the pseudo-projective curvature tensor in these structures. Additionally, the paper extends its analysis to examine the behavior of the pseudo-projective curvature tensor in the context of generalized doubly and twiste

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Pusic, Nevena. "A note on curvature-like invariants of some connections on locally decomposable spaces." Publications de l'Institut Math?matique (Belgrade) 94, no. 108 (2013): 219–28. http://dx.doi.org/10.2298/pim1308219p.

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We consider an n-dimensional locally product space with p and q dimensional components (p + q = n) with parallel structure tensor, which means that such a space is locally decomposable. If we introduce a conformal transformation on such a space AB, it will have an invariant curvature-type tensor, the so-called product conformal curvature tensor (PC-tensor). Here we consider two connections, (F, g)-holomorphically semisymmetric one and F-holomorphically semisymmetric one, both with gradient generators. They both have curvature-like invariants and they are both equal to PC-tensor.

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MANEV, MANCHO. "NATURAL CONNECTION WITH TOTALLY SKEW-SYMMETRIC TORSION ON ALMOST CONTACT MANIFOLDS WITH B-METRIC." International Journal of Geometric Methods in Modern Physics 09, no. 05 (2012): 1250044. http://dx.doi.org/10.1142/s0219887812500442.

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A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this connection, when the corresponding curvature tensor has the properties of the curvature tensor for the Levi-Civita connection and the torsion tensor is parallel, are obtained.

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Lukic, Katarina. "The Jacobi-orthogonality in indefinite scalar product spaces." Publications de l'Institut Math?matique (Belgrade) 115, no. 129 (2024): 33–44. http://dx.doi.org/10.2298/pim2429033l.

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We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that every quasi-Clifford tensor is Jacobi-orthogonal. We prove that a Jacobi-diagonalizable Jacobi-orthogonal tensor is Jacobi-dual whenever JX has no null eigenvectors for all nonnull X. We show that any algebraic curvature tensor of dimension 3 is Jacobi-orthogonal if and only if it is of constant sectional curvature. We prove that every 4-dimensional Jacobidia

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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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Bashashina, K. "Curvature tensor of connection in principal bundle of Cartan's projective connection space." Differential Geometry of Manifolds of Figures, no. 50 (2019): 36–40. http://dx.doi.org/10.5922/10.5922/0321-4796-2019-50-5.

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We considered Cartan's projective connection space with structure equations generalizing the structure equations of the projective space and the condition of local projectivity (this condition is an analogue to the equiprojectivity condition in the projective space). The curvature-torsion object of the space is a tensor containing three subtensor: torsion tensor, torsion affine curvature tensor, extended torsion tensor. Cartan's projective connection space is not a space with connection of the principal bundle. The assignment of a connection in the adjoint principal bundle leads to a space wit

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De, Uday, Young Suh, Sudhakar Chaubey, and Sameh Shenawy. "On pseudo H-symmetric Lorentzian manifolds with applications to relativity." Filomat 34, no. 10 (2020): 3287–97. http://dx.doi.org/10.2298/fil2010287d.

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In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-symmetric manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian manifolds. Also, we provide several interesting results. Among others, we prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar curvature of

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Creţu, Georgeta. "New classes of projectively related Finsler metrics of constant flag curvature." International Journal of Geometric Methods in Modern Physics 17, no. 05 (2020): 2050068. http://dx.doi.org/10.1142/s0219887820500681.

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We define a Weyl-type curvature tensor of [Formula: see text]-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel functions. Based on this aspect, we construct new families of projectively related Finsler metrics that have constant flag curvature.

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