Developments of curves with respect to symmetric tensors and existence of isometric immersions with prescribed second fundamental form

2019/11/18 by Chengjie Yu, Yu, Chengjie
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1911.07493

openalex publication_date 2019/11/18 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the notion of developments of curves with respect to symmetric tensors and use it to prove the existence of isometric immersions into a general ambient space with prescribed second fundamental form. Our method provides a geometric construction of such an isometric immersion.

Citations

• A Bonnet theorem for isometric immersions into products of space forms
• Isometric immersions into products of space forms

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