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We determine necessary conditions for a non-horizontal submanifold of asub-Riemannian stratified Lie group to be of minimal measure. We calculate thefirst variation of the measure for a non-horizontal submanifold and find thatthe minimality condition implies the tensor equation $H+\sigma=0$, where $H$ isanalogous to the mean curvature and $\sigma$ is the mean torsion. We alsodiscuss new examples of minimal non-horizontal submanifolds in the Heisenberggroup, in particular surfaces in $\mathbb H^2$.

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