Pseudo-Bochner curvature tensor on Hermitian manifolds
Matsuo, Koji
Colloquium Mathematicae, Tome 79 (1999), p. 201-209 / Harvested from The Polish Digital Mathematics Library
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Our main purpose of this paper is to introduce a natural generalization BH of the Bochner curvature tensor on a Hermitian manifold M provided with the Hermitian connection. We will call BH 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 BH is naturally obtained from the conformal relation for the pseudo-curvature tensor P and it is conformally invariant. Moreover we show that BH is different from the Bochner conformal tensor in the sense of Tricerri and Vanhecke.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:210712 
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     title = {Pseudo-Bochner curvature tensor on Hermitian manifolds},
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     volume = {79},
     year = {1999},
     pages = {201-209},
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Matsuo, Koji. Pseudo-Bochner curvature tensor on Hermitian manifolds. Colloquium Mathematicae, Tome 79 (1999) pp. 201-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p201bwm/

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