On the axiom of spheres in Kahler geometry

TL;DR

This paper extends known results in Kahler geometry by showing that certain curvature conditions imply constant holomorphic sectional curvature under weaker assumptions.

Contribution

It generalizes previous theorems by relaxing the conditions needed to conclude constant holomorphic sectional curvature in Kahler manifolds.

Findings

Axiom of holomorphic 2n-spheres implies constant curvature

Axiom of antiholomorphic n-spheres implies constant curvature

Results hold under weaker assumptions than previously established

Abstract

It is known, that if a 2m-dimensional Kahler manifold satisfies the axiom of holomorphic 2n-spheres (1<n<m) or the axiom of antiholomorphic n-spheres (2<n), it is of constant holomorphic sectional curvature. In this paper the same result is obtained under weaker assumptions.