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A theorem of Archimedes about spheres and cylinders and two-point homogeneous spaces

Published online by Cambridge University Press:  17 April 2009

M. Djorić  and
L. Vanhecke
M. Djorić
Affiliation:
Faculty of Mathematics, University of Belgrade, P.B. 550 Studentski trg 16 11000 Belgrade, Yugoslavia
L. Vanhecke
Affiliation:
Department of Mathematics Katholieke, Universiteit Leuven Celestijnenlaan, 200B B-3001 Leuven, Belgium
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Abstract

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Starting from the well-known classical theorem of Archimedes about the volumes of spheres and circumscribing cylinders in three-dimensional Euclidean space, one considers circumscribing tubes of small geodesic spheres in general Riemannian manifolds and one derives new characterisations of two-point homogeneous spaces from it.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 283 - 294
Copyright
Copyright © Australian Mathematical Society 1991

References

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