Fundamental Theorem for Submanifolds in General Ambient Spaces

Chengjie Yu

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arXiv · 2109.03474

Fundamental Theorem for Submanifolds in General Ambient Spaces

Chengjie Yu

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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.

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Chengjie Yu. 2021-09-08. Fundamental Theorem for Submanifolds in General Ambient Spaces. https://arxiv.org/abs/2109.03474

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