Submanifolds with Biharmonic Gauss Map
A. Balmu\c{s}, S. Montaldo, and C. Oniciuc
TL;DR
This paper characterizes submanifolds in Euclidean spaces that have proper biharmonic Gauss maps and provides explicit examples of such hypersurfaces.
Contribution
It generalizes the Ruh-Vilms problem by identifying conditions for biharmonic Gauss maps and constructing specific hypersurface examples.
Findings
Characterization of submanifolds with proper biharmonic Gauss maps
Construction of explicit hypersurface examples
Extension of Ruh-Vilms problem results
Abstract
We generalize the Ruh-Vilms problem by characterizing the submanifolds in Euclidean spaces with proper biharmonic Gauss map and we construct examples of such hypersurfaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds