Pseudo-Bochner curvature tensor on Hermitian manifolds

• Autorzy: Koji Matsuo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hermitian manifold   Hermitian connection   pseudo-Bochner curvature tensor   (Hermitian) pseudo-curvature tensor  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 2
• Strony: 201-209

Daty

wydano

1999

otrzymano

1998-10-13

Twórcy

autor

Koji Matsuo

• Department of Mathematics, Ichinoseki National College of Technology, Ichinoseki 021-8511, Japan

Bibliografia

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• [8] S. Tachibana, On the Bochner curvature tensor, Nat. Sci. Rep. Ochanomizu Univ. 18 (1967), 15-19.
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