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On antipodes on a
manifold endowed with a generic Riemannian metric
Joël Rouyer |
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Vol. 212 (2003), No. 1, 187–200
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Abstract |
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We prove that a generic point of a Cr manifold endowed with a generic Riemannian structure has an unique antipode (i.e., farthest point). Furthermore, in the case of 2-dimensional manifolds, such a point is joined to its antipode by at most three minimizing geodesics (r ≥ 2). |
Milestones
Received: 3 April 2002
Revised: 4 November 2002
Published: 1 November 2003
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Authors |
| Joël Rouyer | |
| Laboratoire de Mathématiques et
Applications Faculté des Sciences et Techniques - Université de Haute-Alsace 4, rue des frères Lumière F-68 093 Mulhouse Cedex France |
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