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Anti-invariant Riemannian submersions from almost Hermitian manifolds

100%

Ṣahin B.

Open Mathematics

2010

tom 8

nr 3

437-447

We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.

Pseudo-Bochner curvature tensor on Hermitian manifolds

100%

Matsuo K.

Colloquium Mathematicum

1999

tom 80

nr 2

201-209

Our main purpose of this paper is to introduce a natural generalization $B_H$ of the Bochner curvature tensor on a Hermitian manifold $M$ provided with the Hermitian connection. We will call $B_H$ the pseudo-Bochner curvature tensor. Firstly, we introduce a unique tensor P, called the (Hermitian) pseudo-curvature tensor, which has the same symmetries as the Riemannian curvature tensor on a Kähler manifold. By using P, we derive a necessary and sufficient condition for a Hermitian manifold to be of pointwise constant Hermitian holomorphic sectional curvature. Our pseudo-Bochner curvature tensor $B_H$ is naturally obtained from the conformal relation for the pseudo-curvature tensor P and it is conformally invariant. Moreover we show that $B_H$ is different from the Bochner conformal tensor in the sense of Tricerri and Vanhecke.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

1 Matsuo K.

1 Ṣahin B.

1 2010

1 1999

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Anti-invariant Riemannian submersions from almost Hermitian manifolds

Pseudo-Bochner curvature tensor on Hermitian manifolds