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Krümmungseigenschaften transnormaler Mannigfaltigkeiten

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Abstract

In [6] ROBERTSON introduced the notion of a transnormal manifold as a generalization of a compact connected closed hypersurface of constant width in Euclidean space. This paper includes a detailed proof of the fact that the projection of a transnormal manifold on its space of normal planes is a covering map. Furthermore we prove the following generalization of a property of closed convex hypersurfaces of constant width: If two points p, q of a transnormal manifold have the same normal plane, then (for a suitable choice) the sum of the corresponding radii of principal curvature in direction of the common normal line is equal to the distance of p and q. Finally there are given examples of transnormal manifolds, which do not possess minimal total absolute curvature.

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Authors and Affiliations

  1. Technische Universität Berlin Mathematisches Institut, Straße des 17. Juni 135, 1 Berlin 12

    Bernd Wegner

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  1. Bernd Wegner
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Die vorliegende Arbeit stellt im wesentlichen die ersten Kapitel der von der Fakultät für Allgemeine Ingenieurwissenschaften der TU Berlin genehmigten Dissertation [9] dar.

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Wegner, B. Krümmungseigenschaften transnormaler Mannigfaltigkeiten. Manuscripta Math 3, 375–390 (1970). https://doi.org/10.1007/BF01168293

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  • DOI: https://doi.org/10.1007/BF01168293

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