Isometric immersions with flat normal bundle between space forms

2020/08/10 by Marcos Dajczer, Christos-Raent Onti, Dajczer, M. +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2008.03929

openalex publication_date 2020/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the behavior of the second fundamental form of an isometric immersion of a space form with negative curvature into a space form so that the extrinsic curvature is negative. If the immersion has flat normal bundle, we prove that its second fundamental form grows exponentially.

Cited by

• Submanifolds of Constant Negative Curvature: A Generalization of Hilbert's Theorem

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