On a projective conformal semi-symmetric connection

Cui, Jingshi; Chol, Jon Yong; Tal, Ho Yun; Zhao, Peibiao

doi:10.2298/fil1912901c

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Based on relations (4.9) and (4.14), we conclude that curvature tensor ∇ is conjugate symmetric (see [5]). From here we see that the connection Remark 4.1 In paper [24], the authors observed quarter-symmetric non-metric connection in the form…”

Section: Properties Of Curvature Tensorsmentioning

confidence: 75%

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Quarter-symmetric non-metric connection

Maksimović¹

2022

Preprint

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The paper will study a new quarter-symmetric non-metric connection on a generalized Riemannian manifold. It will determine the relations that the torsion tensor satisfies. The exterior derivative of the skew-symmetric part F of generalized metric G with respect to the Levi-Civita connection coincides with that of skew-symmetric part F with respect to quarter-symmetric non-metric connection, which implies that the even-dimensional manifold endowed with F is symplectic manifold if and only if it is closed with respect to quarter-symmetric non-metric connection. The linearly independent curvature tensors of this connection and its dual (conjugate) connection are determined and the properties of these tensors are discussed. Finally, the condition is given that the connection should be conjugate symmetric.

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Section: Properties Of Curvature Tensorsmentioning

confidence: 75%

“…This connection was also studied in papers [4,5]. These papers motivated us to study the quarter-symmetric connection on the generalized Riemannian manifold in the following form…”

Section: Introductionmentioning

confidence: 99%

Quarter-symmetric non-metric connection

Maksimović¹

2022

Preprint

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“…Some other geometric object can be defined using curvature tensor, for example Ricci curvature tensor, scalar curvature, Weyl tensor, etc. In the articles [2,3,20], the curvature tensor was studied at various mappings and transformations (see also the monographs [4] and [7]).…”

Section: Introductionmentioning

confidence: 99%

Some New Identities for the Second Covariant Derivative of the Curvature Tensor

Maksimović

Stankovic

2021

FU Math Inform

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In this paper we study the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum.

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