On the Sum of the Hermitian Scalar Curvatures of a Compact Hermitian Manifold.

Andrew Balas

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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...