具有全测地纤维的半黎曼浸没
微分几何
2010-01-25 v4
摘要
在纤维维数小于等于三且纤维上诱导的度量为负定的假设下,我们将从实伪双曲空间到半黎曼流形的具有连通全测地纤维的半黎曼浸没进行分类。同时,在纤维维数小于等于二且纤维上诱导的度量为负定的假设下,我们得到了从复伪双曲空间到半黎曼流形的具有连通复全测地纤维的半黎曼浸没的分类。我们证明了不存在从四元数伪双曲空间到黎曼流形的具有连通四元数纤维的半黎曼浸没。
引用
@article{arxiv.math/0005254,
title = {Semi-Riemannian submersions with totally geodesic fibres},
author = {Gabriel Baditoiu},
journal= {arXiv preprint arXiv:math/0005254},
year = {2010}
}
备注
25 pages. Corrections: In some statements, metrics induced on fibres are now assumed to be negative definite. Lemma 3.12 of the previous version is removed