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Displaying similar documents to “The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor”

Pseudo-Bochner curvature tensor on Hermitian manifolds

Koji Matsuo (1999)

Colloquium Mathematicae

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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...

Extended Derdziński-Shen theorem for curvature tensors

Carlo Alberto Mantica, Luca Guido Molinari (2012)

Colloquium Mathematicae

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We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.