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Second Variation of Sub-Riemannian Surface Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups

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Abstract

We establish the second variation of sub-Riemannian surface measure for minimal non-horizontal submanifolds of a sub-Riemannian stratified Lie group. We obtain some applications for codimension one. Furthermore, we present a new proof of the fact that the hyperbolic paraboloid is stable in the Heisenberg group.

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Funding

This work has been partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Grant 428299/2018-0.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Amazonas, Av. General Rodrigo Octávio, 6200 - Coroado I, Manaus, 69077-000, Amazonas, Brazil

    Maria R. B. Santos

  2. Faculdade de Matemática, Universidade Federal do Pará, Rua Augusto Corrêa, 1 - Guamá, Belém, 66075-110, Pará, Brazil

    José M. M. Veloso

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  1. Maria R. B. Santos
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  2. José M. M. Veloso
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Correspondence to Maria R. B. Santos.

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José M. M. Veloso contributed equally to this work.

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Santos, M.R.B., Veloso, J.M.M. Second Variation of Sub-Riemannian Surface Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups. J Dyn Control Syst 29, 721–756 (2023). https://doi.org/10.1007/s10883-022-09606-0

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