Holomorphic isometry from a Kahler manifold into a product of complex projective manifolds

TL;DR

This paper investigates the properties of local holomorphic isometric maps from certain Kahler manifolds into products of projective algebraic manifolds with Fubini-Study metrics, including cases with negative isometric factors.

Contribution

It provides new insights into the global behavior of holomorphic isometries into product manifolds with mixed metric signs.

Findings

Characterization of holomorphic isometries with negative factors

Conditions for global extension of local isometries

Structural properties of mappings into product manifolds

Abstract

We study the global property of local holomorphic isometric mappings from a class of Kahler manifolds into a product of projective algebraic manifolds with induced Fubini-Study metrics, where isometric factors are allowed to be negative.