Principal elliptic bundles and compact homogeneous l.c.K. manifolds
Abstract
In this paper, we provide a systematic and constructive description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds. From this description we explicitly classify homogeneous l.c.K. structures on compact homogeneous Hermitian manifolds using elements of representation theory of complex simple Lie algebras. Moreover, we also describe using Lie theory all homogeneous solutions of the Hermitian-Einstein-Weyl equation on compact homogeneous Hermitian-Weyl manifolds. As an application, we provide a huge class of explicit (nontrivial) examples of such structures on homogeneous Hermitian manifolds, these examples include elliptic bundles over full flag manifolds, elliptic bundles over Grassmannian manifolds, and 8-dimensional locally conformal hyperK\"{a}hler compact manifolds.
Keywords
Cite
@article{arxiv.1904.10099,
title = {Principal elliptic bundles and compact homogeneous l.c.K. manifolds},
author = {Eder M. Correa},
journal= {arXiv preprint arXiv:1904.10099},
year = {2022}
}
Comments
32 pages; This current version is a reduced version of the previous paper (which was splitted into two shorter papers). It contains the main results of the previous version. Some minor corrections were made. Comments are welcome