主椭圆丛与紧齐性l.c.K.流形
微分几何
2022-03-28 v2 代数几何
摘要
本文对复旗流形上某些主椭圆丛上的Vaisman结构给出了系统且构造性的描述。基于此描述，我们利用复单李代数表示论的元素显式分类了紧齐性Hermitian流形上的齐性l.c.K.结构。此外，我们还利用李理论描述了紧齐性Hermitian-Weyl流形上Hermitian-Einstein-Weyl方程的所有齐性解。作为一个应用，我们给出了一大类齐性Hermitian流形上此类结构的显式（非平凡）例子，这些例子包括全旗流形上的椭圆丛、Grassmannian流形上的椭圆丛，以及8维局部共形超Kähler紧流形。
引用
@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}
}
备注
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