On Sasakian manifolds, Matsumoto and Chūman [3] defined a contact Bochner curvature tensor (see also Yano [7]) which is invariant under D-homothetic deformations (for D-homothetic deformations, see Tanno [5]). On the other hand, Tricerri and Vanhecke [6] defined a general Bochner curvature tensor with conformal invariance on almost Hermitian manifolds. In this paper we define an extended contact Bochner curvature tensor which is invariant under D-homothetic deformations of contact metric manifolds; we call it the EK-contact Bochner curvature tensor. We show that a contact metric manifold with vanishing EK-contact Bochner curvature tensor is a Sasakian manifold.
@article{bwmeta1.element.bwnjournal-article-cmv65i1p33bwm,
author = {Hiroshi Endo},
title = {On an extended contact Bochner curvature tensor on contact metric manifolds},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {33-41},
zbl = {0820.53041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv65i1p33bwm}
}
Endo, Hiroshi. On an extended contact Bochner curvature tensor on contact metric manifolds. Colloquium Mathematicae, Tome 66 (1993) pp. 33-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv65i1p33bwm/
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