The Density Property for Vector Bundles

TL;DR

This paper demonstrates that holomorphic vector bundles over Stein manifolds with the density property also have the density property if their total space is holomorphically flexible, leading to new examples of Stein manifolds with this property.

Contribution

It establishes a link between the density property of Stein manifolds and their vector bundles under holomorphic flexibility, expanding the class of manifolds known to have the density property.

Findings

Holomorphic vector bundles over Stein manifolds with the density property also have the density property under certain conditions.

Provides new examples of Stein manifolds with the density property.

Connects the concepts of density property and holomorphic flexibility in complex geometry.

Abstract

We prove that holomorphic vector bundles over Stein manifolds with the density property also satisfy the density property, provided that the total space is holomorphically flexible. We apply this result to provide a new class of Stein manifolds with the density property.