Conformally Kähler surfaces and orthogonal holomorphic bisectional curvature

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

un 2 00 6 On Kähler manifolds with positive orthogonal bisectional curvature

The famous Frankel conjecture asserts that any compact Kähler manifold with positive bisectional curvature must be biholomorphic to CP n. This conjecture was settled affirmatively in early 1980s by two groups of mathematicians independently: Siu-Yau[16] via differential geometry method and Morri [15] by algebraic method. There are many interesting papers following this celebrated work; in parti...

Characterization of Holomorphic Bisectional Curvature of GCR-Lightlike Submanifolds

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite comple...

The Holomorphic Bisectional Curvature of the Complex Finsler Spaces

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

The Kähler - Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator