Intrinsic Invariants of Cross Caps
Differential Geometry
2012-11-13 v2
Abstract
It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap (u,uv,v^2) has non-trivial isometric deformations with infinite dimensional freedom. Since there are several geometric invariants for cross caps, the existence of isometric deformations suggests that one can ask which invariants of cross caps are intrinsic. In this paper, we show that there are three fundamental intrinsic invariants for cross caps. The existence of extrinsic invariants is also shown.
Keywords
Cite
@article{arxiv.1207.3853,
title = {Intrinsic Invariants of Cross Caps},
author = {Masaru Hasegawa and Atsufumi Honda and Kosuke Naokawa and Masaaki Umehara and Kotaro Yamada},
journal= {arXiv preprint arXiv:1207.3853},
year = {2012}
}
Comments
16 pages, 6 figures