Local classification of K\"ahler metrics with constant holomorphic sectional curvature

TL;DR

This paper provides a local classification of Kähler metrics with constant holomorphic sectional curvature using the geometry of the bundle of 1-jets of holomorphic functions.

Contribution

It introduces a novel approach by exploiting jet bundle geometry to classify Kähler metrics with constant holomorphic sectional curvature.

Findings

Achieved a comprehensive local classification of such Kähler metrics.

Connected jet bundle geometry with curvature properties.

Provided new insights into the structure of Kähler manifolds with constant curvature.

Abstract

We prove the local classification of K\"ahler metrics with constant holomorphic sectional curvature by exploiting the geometry of the bundle of 1-jets of holomorphic functions.