The K\"ahler submanifolds between the ball bundles and the complex Euclidean space

TL;DR

This paper establishes conditions under which certain Kähler submanifolds cannot exist between complex Euclidean spaces and ball bundles over Kähler manifolds, leading to non-existence results for specific classes of these bundles.

Contribution

It provides new sufficient conditions for the non-existence of common Kähler submanifolds between Euclidean space and ball bundles over Kähler manifolds, extending previous non-existence theorems.

Findings

Non-existence theorems for Kähler submanifolds in specific ball bundles

Conditions on Hermitian vector bundles over Kähler manifolds

Applications to Hermitian symmetric spaces and Kähler-Einstein manifolds

Abstract

In this paper, we provide a sufficient condition on the non-existence of the common K\"ahler submanifolds between the complex Euclidean space and the ball bundles of some Hermitian vector bundles over K\"ahler manifolds. Then we get the non-existence theorems on several classes of ball bundles whose base spaces are Hermitian symmetric spaces or the complete K\"ahler-Einstein manifolds.