- Tytuł:
- Pseudo-Bochner curvature tensor on Hermitian manifolds
- Autorzy:
- Matsuo, Koji
- Powiązania:
- https://bibliotekanauki.pl/articles/965855.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Hermitian manifold
Hermitian connection
pseudo-Bochner curvature tensor
(Hermitian) pseudo-curvature tensor - Opis:
- 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.
- Źródło:
-
Colloquium Mathematicum; 1999, 80, 2; 201-209
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł