Extensions of isometric immersions and Cartan-Ambrose-Hicks theorem based on submanifolds

TL;DR

This paper extends the Cartan-Ambrose-Hicks theorem to isometric immersions based on submanifolds, offering new geometric methods for constructing such extensions.

Contribution

It introduces a generalized extension framework for isometric immersions using submanifolds, expanding classical theorems with novel geometric constructions.

Findings

Established new Cartan-Ambrose-Hicks theorems based on submanifolds

Provided geometric methods for constructing extensions of isometric immersions

Enhanced understanding of the extension problem in differential geometry

Abstract

In this paper, we study the general extension problem for isometric immersions by establishing Cartan-Ambrose-Hicks theorems based on submanifolds. Our method also provides geometric constructions of such extensions.