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  1. 3 Colloquium Mathematicum

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  1. 3 Endo H.

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  1. 1 1993

  2. 1 1991

  3. 1 1989

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On an extended contact Bochner curvature tensor on contact metric manifolds

100%
Endo H.
Colloquium Mathematicum
|
1993
|
tom 65
|
nr 1
33-41
EN
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.
2
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On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor

100%
Endo H.
Colloquium Mathematicum
|
1991
|
tom 62
|
nr 2
293-297
EN
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.
3
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On invariant submanifolds in almost cosymplectic manifolds

44%
Endo H.
Colloquium Mathematicum
|
1989
|
tom 57
|
nr 1
69-72
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