Fundamental Theorem for Submanifolds in General Ambient Spaces
Differential Geometry
2025-03-11 v3
Abstract
In this paper, we extend the fundamental theorem for submanifolds to general ambient spaces by viewing it as a higher codimensional Cartan-Ambrose-Hicks theorem. The key ingredient in obtaining this is a generalization of development of curves in the positive codimensional case. One advantage of our results is that it also provide a geometric construction of the isometric immersion when the isometric immersion exists.
Cite
@article{arxiv.2109.03474,
title = {Fundamental Theorem for Submanifolds in General Ambient Spaces},
author = {Chengjie Yu},
journal= {arXiv preprint arXiv:2109.03474},
year = {2025}
}
Comments
Some of the results are strengthen and the paper are rewritten into arXiv:1911.13242 and 1911.07493