充分坍塌的不可约Alexandrov三维空间是几何的
微分几何
2020-05-21 v2 度量几何
摘要
我们证明充分坍塌、闭且不可约的三维Alexandrov空间以八种三维Thurston几何之一为模型。这将Shioya和Yamaguchi最初针对黎曼流形表述的结果推广到了Alexandrov设置。
关键词
引用
@article{arxiv.1709.02336,
title = {Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric},
author = {Fernando Galaz-Garcia and Luis Guijarro and Jesús Núñez-Zimbrón},
journal= {arXiv preprint arXiv:1709.02336},
year = {2020}
}
备注
We have added a proof of the fact that a closed collapsing Alexandrov 3-space cannot admit hyperbolic geometry (see Remark B). This improves our main Theorem (Theorem A) by ruling out the appearance of hyperbolic geometry. 24 pages, 3 Tables