• Korean Journal of Mathematics
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• 제10권2호
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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.

• 대한수학회논문집
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• 제13권2호
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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.

• 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.

• 대한수학회논문집
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• 제31권1호
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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.

• 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.

• East Asian mathematical journal
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• 제8권1호
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• pp.55-58
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• 1992

• 대한수학회논문집
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• 제8권4호
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• pp.689-697
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• 1993

• Kyungpook Mathematical Journal
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• 제29권2호
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• pp.187-198
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• 1989

• 대한수학회지
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• 제28권2호
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• pp.267-274
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• 1991