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.
@article{bwmeta1.element.bwnjournal-article-cmv62i2p293bwm,
author = {Hiroshi Endo},
title = {On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor},
journal = {Colloquium Mathematicae},
volume = {62},
year = {1991},
pages = {293-297},
zbl = {0796.53051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv62i2p293bwm}
}
Endo, Hiroshi. On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor. Colloquium Mathematicae, Tome 62 (1991) pp. 293-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv62i2p293bwm/
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