• Title/Summary/Keyword: contact conformal curvature tensor

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VANISHING OF CONTACT CONFORMAL CURVATURE TENSOR ON 3-DIMENSIONAL SASAKIAN MANIFOLDS

  • Bang, Keumseong;Kye, JungYeon
    • Korean Journal of Mathematics
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    • v.10 no.2
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    • pp.157-166
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    • 2002

  • We show that the contact conformal curvature tensor on 3-dimensional Sasakian manifold always vanishes. We also prove that if the contact conformal curvature tensor vanishes on a 3-dimensional locally ${\varphi}$-symmetric contact metric manifold M, then M is a Sasakian space form.

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A NOTE ON CONTACT CONFORMAL CURVATURE TENSOR

  • Pak, Jin-Suk;Shin, Yang-Jae
    • Communications of the Korean Mathematical Society
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    • v.13 no.2
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    • pp.337-343
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    • 1998

  • In this paper we show that every contact metric manifold with vanishing contact conformal curvature tensor is a Sasakian space form.

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ON THE CONTACT CONFORMAL CURVATURE TENSOR$^*$

  • Jeong, Jang-Chun;Lee, Jae-Don;Oh, Ge-Hwan;Park, Jin-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.27 no.2
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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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ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS

  • Baishya, Kanak Kanti;Chowdhury, Partha Roy
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.163-176
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    • 2016

  • The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

  • https://doi.org/10.4134/CKMS.2016.31.1.163 인용 PDF KSCI

A CURVATURE-LIKE TENSOR FIELD ON A SASAKIAN MANIFOLD

  • Kim, Young-Mi
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.1
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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