A note on compact solvmanifolds with Kaehler structures
Complex Variables
2016-01-19 v1 Differential Geometry
Symplectic Geometry
Abstract
A solvmanifold is a compact differentiable manifold M on which a connected solvable Lie group G acts transitively. As the main result, we will see, applying a result of Arapura and Nori on solvable Kaehler groups and some of the author's previous results, that a compact solvmanifold admits a Kaehler structure if and only if it is a finite quotient of a complex torus which has a structure of a complex torus bundle over a complex torus. There are also quite a few comments and remarks on and around this result.
Cite
@article{arxiv.math/0406227,
title = {A note on compact solvmanifolds with Kaehler structures},
author = {Keizo Hasegawa},
journal= {arXiv preprint arXiv:math/0406227},
year = {2016}
}
Comments
7 pages