Sub-Riemannian structures on 3D Lie groups

Details Sub-Riemannian structures on 3D Lie groups Sub-Riemannian structures on 3D Lie groups

2010-07-28

arxiv.org/abs/1007.4970v2

Mathematics

Differential Geometry

Scientific paper

We give a complete classification of left-invariant sub-Riemannian structures
on three dimensional Lie groups in terms of the basic differential invariants.
As a corollary we explicitly find a sub-Riemannian isometry between the
nonisomorphic Lie groups SL(2) and $A^+(\R)\times S^1$, where $A^+(\R)$ denotes
the group of orientation preserving affine maps on the real line.

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