• 제목/요약/키워드: conformal curvature tensor field

검색결과 17건 처리시간 0.025초

ON THE CONTACT CONFORMAL CURVATURE TENSOR$^*$

  • Jeong, Jang-Chun;Lee, Jae-Don;Oh, Ge-Hwan;Park, Jin-Suk
    • 대한수학회보
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    • 제27권2호
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    • pp.133-142
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    • 1990

  • In this paper, we define a new tensor field on a Sasqakian manifold, which is constructed from the conformal curvature tensor field by using the Boothby-Wang's fibration ([3]), and study some properties of this new tensor field. In Section 2, we recall definitions and fundamental properties of Sasakian manifold and .phi.-holomorphic sectional curvature. In Section 3, we define contact conformal curvature tensor field on a Sasakian manifold and prove that it is invariant under D-homothetic deformation due to S. Tanno([13]). In Section 4, we study Sasakian manifolds with vanishing contact conformal curvature tensor field, and the last Section 5 is devoted to studying some properties of fibred Riemannian spaces with Sasakian structure of vanishing contact conformal curvature tensor field.

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LOCALLY PRODUCT INDEFINITE KAEHLERIAN METRICS WITH VANISHING CONFORMAL CURVATURE TENSOR FIELD

  • Kwon, Jung-Hwan;Sohn, Won-Ho
    • 대한수학회보
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    • 제29권1호
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    • pp.25-29
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    • 1992

  • The purpose of this paper is to study indefinite Kaehlerian metrics with vanishing conformal curvature tensor field. In the first section, a brief summary of the complex version of indefinite Kaehlerian manifolds is recalled and we introduce the conformal curvature tensor field on an indefinite Kaehlerian manifold. In section 2, we obtain the theorem for indefinite Kaehlerian metrics with vanishing conformal curvature tensor field.

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STUDY OF P-CURVATURE TENSOR IN THE SPACE-TIME OF GENERAL RELATIVITY

  • Ganesh Prasad Pokhariyal;Sudhakar Kumar Chaubey
    • 호남수학학술지
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    • 제45권2호
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    • pp.316-324
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    • 2023

  • The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P𝛼𝛽. It is established that the divergence of tensor G𝛼𝛽 defined with the help of P𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V4 satisfying Einstein like field equations, the tensor P𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

  • https://doi.org/10.5831/HMJ.2023.45.2.316 인용 PDF

A CURVATURE-LIKE TENSOR FIELD ON A SASAKIAN MANIFOLD

  • Kim, Young-Mi
    • 대한수학회보
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    • 제43권1호
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    • pp.81-99
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    • 2006

  • We investigate a curvature-like tensor defined by (3.1) in Sasakian manifold of $dimension{\geq}$ 5, and show that this tensor satisfies some properties. Especially, we determine compact Sasakian manifolds with vanishing this tensor and improve some theorems concerning contact conformal curvature tensor and spectrum of Laplacian acting on $p(0{\leq}P{\leq}2)-forms$ on the manifold by using this tensor component.

  • https://doi.org/10.4134/BKMS.2006.43.1.081 인용 PDF KSCI