Holomorphic projective connections on compact complex threefolds
Differential Geometry
2023-04-25 v2 Algebraic Geometry
Abstract
We prove that a holomorphic projective connection on a complex projective threefold is either flat, or it is a translation invariant holomorphic projective connection on an abelian threefold. In the second case, a generic translation invariant holomorphic affine connection on the abelian variety is not projectively flat. We also prove that a simply connected compact complex threefold with trivial canonical line bundle does not admit any holomorphic projective connection.
Cite
@article{arxiv.2005.08272,
title = {Holomorphic projective connections on compact complex threefolds},
author = {Indranil Biswas and Sorin Dumitrescu},
journal= {arXiv preprint arXiv:2005.08272},
year = {2023}
}
Comments
This is the final version to appear in Math. Zeitschrift