Local classification of Kähler metrics with constant holomorphic sectional curvature enhances our understanding of complex geometry.
The classification specifically relies on the geometry of the bundle of holomorphic functions, indicating connections within metric properties.
Exploration of holomorphic functions and their jets facilitates insights into Kähler metrics' structure and behaviors.
This study highlights the interplay between curvature properties and holomorphic functions in the context of complex manifolds.
Resumen
ABSTRACT We prove the local classification of Kähler metrics with constant holomorphic sectional curvature by exploiting the geometry of the bundle of 1-jets of holomorphic functions.