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Ovaloids whose curvatures are powers of support functions

Part of: Global differential geometry

Published online by Cambridge University Press:  26 February 2010

Chr. Georgiou  and
Th. Hasanis
Chr. Georgiou
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina, Greece.
Th. Hasanis
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina, Greece.
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Extract

Let Mn be a smooth, compact and strictly convex, embedded hypersurface of Rn + 1 (n ≥ 1), an ovaloid for short. By “strictly convex” we mean that the Gauss-Kronecker curvature where ki are the principal curvatures with respect to the inner unit normal field, is everywhere positive. It is well knpwn [5, p. 41] that, for such a hypersurface, the spherical-image mapping is a diffeomorphism onto the unit hypersphere. Furthermore, Mn is the boundary of an open bounded convex body, which we shall call the interior of Mn.

MSC classification

Secondary: 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)
Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 192 - 197
Copyright
Copyright © University College London 1981

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References

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