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On \(K\)-contact Riemannian manifolds with vanishing \(E\)-contact Bochner curvature tensor. (English) Zbl 0796.53051

The author defines an extended contact Bochner curvature tensor in \(K\)- contact Riemannian manifolds and calls it shortly \(E\)-contact Bochner curvature tensor. In the case of Sasakian manifolds this tensor coincides with the contact Bochner curvature tensor. Moreover, the \(E\)-contact Bochner curvature tensor is an invariant of \(D\)-homothetic deformations of \(K\)-contact structures. The main result of the paper is the following: Every \(K\)-contact Riemannian manifold with vanishing \(E\)-contact Bochner curvature tensor is a Sasakian manifold.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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