Archivio Istituzionale della RicercaWe prove that a compact minimal shadow boundary of a hypersurface in Euclidean space is totally geodesic. We show that shadow boundaries detect principal directions and umbilical points of a hypersurface. As application we deduce that every shadow boundary of a compact strictly convex surface contains at least two principal directions.
A compact minimal shadow boundary in Euclidean space is totally geodesic / DI SCALA, ANTONIO JOSE'; Ruiz Hernandez, G.; Jeronimo Castro, J.. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - STAMPA. - 168:(2012), pp. 183-189. [10.1007/s00605-011-0352-y]
A compact minimal shadow boundary in Euclidean space is totally geodesic
DI SCALA, ANTONIO JOSE';
2012
Abstract
We prove that a compact minimal shadow boundary of a hypersurface in Euclidean space is totally geodesic. We show that shadow boundaries detect principal directions and umbilical points of a hypersurface. As application we deduce that every shadow boundary of a compact strictly convex surface contains at least two principal directions.
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https://hdl.handle.net/11583/2486984
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