Sub-Riemannian manifold

A Sub-Riemannian manifold is a triple $(M,\mathcal{H},g_{\mathcal{H}})$ where $M$ is a manifold, $\mathcal{H}$ is a distribution (that is, a linear subbundle of the tangent bundle $TM$ of $M$), and $g_{\mathcal{H}}$ is a metric on $\mathcal{H}$ induced by a fiber inner product on $\mathcal{H}$. The distribution $\mathcal{H}$ is often referred to as the horizontal distribution.

Title Sub-Riemannian manifold SubRiemannianManifold 2013-03-22 13:58:52 2013-03-22 13:58:52 RevBobo (4) RevBobo (4) 4 RevBobo (4) Definition msc 53C17 Sub-Riemannian geometry