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Submanifolds with Flat Normal Bundle

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Abstract

Let M be a compact orientable submanifold immersed in a Riemannian manifold of constant curvature with flat normal bundle. This paper gives intrinsic conditions for M to be totally umbilical or a local product of several totally umbilical submanifolds. It is proved especially that a compact hypersurface in the Euclidean space with constant scalar curvature and nonnegative Ricci curvature is a sphere.

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Authors
  1. YONGFAN Zheng
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Zheng, Y. Submanifolds with Flat Normal Bundle. Geometriae Dedicata 67, 295–300 (1997). https://doi.org/10.1023/A:1004901125673

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  • DOI: https://doi.org/10.1023/A:1004901125673

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