Submanifolds with totally umbilical Gauss image
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The submanifolds whose Gauss images are totally umbilical submanifolds of the Grassmann manifold are under consideration. The main result is the following classification theorem: if the Gauss image of a submanifold F in a Euclidean space is totally umbilical then either the Gauss image is totally geodesic, or F is the surface in E4 of the special structure. Submanifolds in a Euclidean space with totally geodesic Gauss image were classified earlier.
Mathematics Subject Classifications (1991)53A07 53B25
Key wordsGauss image totally umbilical submanifold
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