Minimalite des sous-varietes totalement geodesiques en geometrie finslerienne

Details Minimalite des sous-varietes totalement geodesiques en geometrie finslerienne Minimalite des sous-varietes totalement geodesiques en geometrie finslerienne

2004-09-18

arxiv.org/abs/math/0409320v1

Mathematics

Differential Geometry

17 pages, 3 figures, in French

Scientific paper

It is shown that if the Holmes-Thompson volume definition is used, totally geodesic submanifolds of a Finsler space are minimal. The analogous result for the Hausdorff measure is known to be false. ----- Nous montrons que les sous-varietes totalement geodesiques d'une variete de Finsler sont minimales pour le volume de Holmes-Thompson. Pour la mesure de Hausdorff, des contre-exemples a ce resultat sont connus.

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