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Semi-symmetric ball-homogeneous spaces and a volume conjecture

Published online by Cambridge University Press:  17 April 2009

G. Calvaruso  and
L. Vanhecke
G. Calvaruso
Affiliation:
Department of MathematicsKatholieke Universiteit LeuvenCelestijnenlaas 200 B3001 LeuvenBelgium
L. Vanhecke
Affiliation:
Department of MathematicsKatholieke Universiteit LeuvenCelestijnenlaas 200 B3001 LeuvenBelgium
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Abstract

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We prove that semi-symmetric ball-homogeneous spaces are locally symmetric and we use this result to prove that a semi-symmetric Riemannian manifold such that the volume of each sufficiently small geodesic ball is the same as in a Euclidean space, is locally flat.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 109 - 115
Copyright
Copyright © Australian Mathematical Society 1998

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