Geodesic
On an extended contact Bochner curvature tensor on contact metric manifolds
Colloquium Mathematicum, Tome 65 (1993) no. 1, pp. 33-41 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm-65-1-33-41

Hiroshi Endo 1

1 
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Hiroshi Endo. On an extended contact Bochner curvature tensor on contact metric manifolds. Colloquium Mathematicum, Tome 65 (1993) no. 1, pp. 33-41. doi: 10.4064/cm-65-1-33-41

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