Sub-Riemannian manifold

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

Title	Sub-Riemannian manifold
Canonical name	SubRiemannianManifold
Date of creation	2013-03-22 13:58:52
Last modified on	2013-03-22 13:58:52
Owner	RevBobo (4)
Last modified by	RevBobo (4)
Numerical id	4
Author	RevBobo (4)
Entry type	Definition
Classification	msc 53C17
Synonym	Sub-Riemannian geometry