Ricci-flat Deformations of Holomorphic Vector Bundles

Abstract

In this paper we give a criterion for a deformation of a hermitian vector bundle to be Ricci-flat. As an application we show that on a Kähler manifold, every deformation of a vector bundle can be made Ricci-flat whereas on some Hopf manifolds, the non-existence of a Ricci-flat deformation is related to non-trivial vector bundles on the universal cover ${\mathbb{C}}^n\setminus \{0\}$. On a surface with $b_1(X)\ne 0$ filtrable Ricci-rigid vector bundles prove to be very special. We apply this to Inoue and Hopf surfaces.

13 pages; Thm 6.6. corrected, more examples included

References in corpus (1)

• Stable bundles on Hopf manifolds