On a holonomy flag of non-holonomic distributions

preprint2015arXivOpen access

We give definition of a holonomy flag in subRiemannian geometry --- a generalization of a Riemannian holonomy algebra --- and calculate it for the 3D subRiemannian Lie groups. We rewrite and give new interpretation for the Codazzi equations for the $(2,3)$ -distributions on the $SU(2)$ and the Heisenberg group.

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On a holonomy flag of non-holonomic distributions

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