A compact minimal shadow boundary in Euclidean space is totally geodesic

A compact minimal shadow boundary in Euclidean space is totally geodesic

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 contai...

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Veröffentlicht in:Monatshefte für Mathematik 2012-11, Vol.168 (2), p.183-189
Hauptverfasser: Di Scala, Antonio J., Jerónimo-Castro, Jesus, Ruiz-Hernández, Gabriel
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-011-0352-y