Symmetries of complex flat manifolds
Abstract
Abstract In this article, we show how to calculate the group of automorphisms of flat Kähler manifolds. Moreover, we are interested in the problem of classification of such manifolds up to biholomorphism. We consider these problems from two points of view. The first one treats the automorphism group as a subgroup of the group of affine transformations, while in the second one, we analyze it using automorphisms of complex tori. This leads us to the analogs of the Bieberbach theorems in the complex case. We end with some examples, which in particular show that in general, the finiteness of the automorphism group depends not only on the fundamental group of a flat manifold.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Physica Scripta
- Publisher
- IOP Publishing
- Volume
- 101
- Issue
- 24
- Pages
- 245202–245202
- Publication date
- 2 June 2026
- Language
- EN