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Journal of Dynamical and Control Systems
Published in: Journal of Dynamical and Control Systems 3/2017

06-08-2016

First Variation of the Hausdorff Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups

Authors: Marcos M. Diniz, Maria R. B. Santos, José M. M. Veloso

Published in: Journal of Dynamical and Control Systems | Issue 3/2017

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Abstract

We determine necessary conditions for a non-horizontal submanifold of a sub-Riemannian stratified Lie group to be of minimal measure. We calculate the first variation of the measure for a non-horizontal submanifold and find that the minimality condition implies the tensor equation H + σ = 0, where H is analogous to the mean curvature and σ is the mean torsion. We also discuss new examples of minimal non-horizontal submanifolds in the Heisenberg group, in particular surfaces in \(\mathbb {H}^{2}\).
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Metadata
Title
First Variation of the Hausdorff Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups
Authors
Marcos M. Diniz
Maria R. B. Santos
José M. M. Veloso
Publication date
06-08-2016
Publisher
Springer US
Published in
Journal of Dynamical and Control Systems / Issue 3/2017
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-016-9339-2

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