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arXiv · 1404.1432

First variation of the Hausdorff measure of non-horizontal submanifolds in stratified Lie groups

Marcos M. Diniz·Maria R. B. Santos·José M. M. Veloso
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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 $H+\sigma=0$, where $H$ is analogous to the mean curvature and $\sigma$ 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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Marcos M. Diniz, Maria R. B. Santos, José M. M. Veloso. 2014-04-05. First variation of the Hausdorff measure of non-horizontal submanifolds in stratified Lie groups. https://arxiv.org/abs/1404.1432

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