Electronic Resource
Springer
Manuscripta mathematica
3 (1970), S. 375-390
ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01168293
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