On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor

Volume 62 / 1991

Hiroshi Endo Colloquium Mathematicum 62 (1991), 293-297 DOI: 10.4064/cm-62-2-293-297

Abstract

For Sasakian manifolds, Matsumoto and Chūman [6] defined the contact Bochner curvature tensor (see also Yano [9]). Hasegawa and Nakane [4] and Ikawa and Kon [5] have studied Sasakian manifolds with vanishing contact Bochner curvature tensor. Such manifolds were studied in the theory of submanifolds by Yano ([9] and [10]). In this paper we define an extended contact Bochner curvature tensor in K-contact Riemannian manifolds and call it the E-contact Bochner curvature tensor. Then we show that a K-contact Riemannian manifold with vanishing E-contact Bochner curvature tensor is a Sasakian manifold.

Authors

  • Hiroshi Endo

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