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- W1978321143 abstract "In this paper we study smooth immersed non-characteristic submanifolds (with or without boundary) of k-step sub-Riemannian Carnot groups, from a differential-geometric point of view. The methods of exterior differential forms and moving frames are extensively used. Particular emphasis is given to the case of hypersurfaces. We state divergence-type theorems and integration by parts formulas with respect to the intrinsic measure σHn−1 on hypersurfaces. General formulas for the first and the second variation of the measure σHn−1 are proved. Dans cet article nous étudions les sous-variétés non caractéristiques (avec ou sans bord) immergées dans un groupe de Carnot sous-riemannien, selon le point de vue de la géométrie différentielle classique, en utilisant la méthode du repère mobile et le formalisme des formes différentielles. En particulier, nous étudions le cas des variétés de codimension 1 en établissant des formules de type divergence et d'intégration par parties par rapport à la mesure intrinsèque σHn−1. Enfin, nous établissons des formules générales pour les variations première et seconde de la mesure σHn−1." @default.
- W1978321143 created "2016-06-24" @default.
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- W1978321143 date "2007-05-01" @default.
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- W1978321143 title "Hypersurfaces and variational formulas in sub-Riemannian Carnot groups" @default.
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- W1978321143 doi "https://doi.org/10.1016/j.matpur.2007.01.009" @default.
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