Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 27 Issue 2
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- Pages.133-142
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- 1990
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
ON THE CONTACT CONFORMAL CURVATURE TENSOR$^*$
- Jeong, Jang-Chun (Yeong Jin Junior College) ;
- Lee, Jae-Don (Taegu University) ;
- Oh, Ge-Hwan (Dongwon Junior College of Tech.) ;
- Park, Jin-Suk (Kyungpook National University)
- Published : 1990.08.01
Abstract
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.
Keywords