Endo, Hiroshi On \(K\)-contact Riemannian manifolds with vanishing \(E\)-contact Bochner curvature tensor. (English) Zbl 0796.53051 Colloq. Math. 62, No. 2, 293-297 (1991). 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. Reviewer: M.Hotloś (Wrocław) Cited in 1 ReviewCited in 3 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:contact Bochner curvature tensor; \(K\)-contact Riemannian manifolds; Sasakian manifolds PDFBibTeX XMLCite \textit{H. Endo}, Colloq. Math. 62, No. 2, 293--297 (1991; Zbl 0796.53051) Full Text: DOI EuDML