Normal curvature of pseudo-umblical submanifolds in a sphere

2019/07/09 by Majid Ali Choudhary, Choudhary, Majid Ali
Mathematics · Physics and Astronomy · #53A10 #53C40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53A10 #msc:53C40

paper · pdf · doi:10.48550/arxiv.1907.06523

arxiv created 2019/07/09 · openalex publication_date 2019/07/09 · arxiv updated 2019/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a compact pseudo-umbilical submanifold of the unit sphere S. In the present note, it is shown that if the normal curvature, scalar curvature S and square of the length of second fundamental form satisfy certain conditions, then M is totally geodesic.

Citations

• Minimal Varieties in Riemannian Manifolds

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