HOLOMORPHIC SECTIONAL AND BISECTIONAL CURVATURES OF ALMOST HERMITIAN MANIFOLDS

Abstract

Friedland and Hsiung [1] proved an analogue of F. Schur’s theorem concerning the holomorphic sectional curvature of some almost Hermitian manifolds called almost Hermitian $L$-manifolds, of which Kählerian manifolds are special ones. Recently, Hsiung and Xiong [3] gave a classification of almost Hermitian manifolds and extended the above work of Friedland and Hsiung to a new class of almost Hermitian manifolds called the class of almost $C$ Hermitian manifolds.

In this paper we shall further extend the above work of Hsiung and Xiong by studying the general sectional, the holomorphic sectional and the holomorphic bisectional curvatures of almost Hermitian manifolds of all classes, together with some relationship among the three types of sectional curvatures.