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

2019/11/27 by Chengjie Yu, Yu, Chengjie
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1911.13242

openalex publication_date 2019/11/27 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28

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.

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