Normal curvature of pseudo-umblical submanifolds in a sphere

2019/07/09 by Choudhary, Majid Ali
#53A10 #53C40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.06523

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.

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