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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Communicated by D. V. Alekseevsky.
G. Ruiz-Hernández was partially supported by Conacyt.
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Di Scala, A.J., Jerónimo-Castro, J. & Ruiz-Hernández, G. A compact minimal shadow boundary in Euclidean space is totally geodesic. Monatsh Math 168, 183–189 (2012). https://doi.org/10.1007/s00605-011-0352-y
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DOI: https://doi.org/10.1007/s00605-011-0352-y