Equivariant strongly projectively flat maps of compact homogeneous K\"ahler manifolds

TL;DR

This paper introduces the concept of strongly projectively flat maps into complex Grassmannians and proves a rigidity theorem for equivariant such maps on compact simply connected homogeneous Kähler manifolds.

Contribution

It generalizes the notion of holomorphic maps into projective space and establishes a rigidity result for equivariant strongly projectively flat maps.

Findings

Defined strongly projectively flatness for holomorphic maps into Grassmannians

Proved a rigidity theorem for equivariant maps on compact homogeneous Kähler manifolds

Extended classical results to a broader class of maps and manifolds

Abstract

In this paper we define strongly projectively flatness of holomorphic maps into the complex Grassmannian manifold, which is a kind of generalization of holomorphic maps into the complex projective space and prove a rigidity of equivariant strongly projectively flat maps of compact simply connected homogeneous K\"ahler manifolds.