Submanifolds with totally umbilical Gauss image
Copyright policy )Submanifolds with totally umbilical Gauss image
The submanifolds whose Gauss images are totally umbilical submanifolds of a Grassmannian manifold are considered. 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 a surface in \(E^n\) of special structure. Submanifolds in Euclidean space with totally geodesic Gauss image were classified earlier.
- University of Melbourne Australia
Local submanifolds, classification, Grassmannian manifold, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, Gauss image, totally umbilical submanifold
Local submanifolds, classification, Grassmannian manifold, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, Gauss image, totally umbilical submanifold
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