On open flat sets in spaces with bipolar comparison
Differential Geometry
2018-08-07 v2
Abstract
We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.
Keywords
Cite
@article{arxiv.1807.02708,
title = {On open flat sets in spaces with bipolar comparison},
author = {Nina Lebedeva},
journal= {arXiv preprint arXiv:1807.02708},
year = {2018}
}