Reduction of manifolds with semi-negative holomorphic sectional curvature

Abstract

In this note, we continue the investigation of a projective Kähler manifold $M$ of semi-negative holomorphic sectional curvature $H$. We introduce a new differential geometric numerical rank invariant which measures the number of linearly independent {\it truly flat} directions of $H$ in the tangent spaces. We prove that this invariant is bounded above by the nef dimension and bounded below by the numerical Kodaira dimension of $M$. We also prove a splitting theorem for $M$ in terms of the nef dimension and, under some additional hypotheses, in terms of the new rank invariant.

References in corpus (2)

• Negative Holomorphic curvature and positive canonical bundle
• An extension of a theorem of Wu-Yau

Cited by in corpus (1)

• Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics