Sub-Riemannian geometry is geometry of the world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach&nbsp;every&nbsp;position from any other.&nbsp;Mathematically this is a smooth manifold equipped with a noninvolutive vector distribution and an Euclidean structure&nbsp;on it.&nbsp;The unconstrained Riemannian world is an important special case. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with motivations and ramifications in several areas of pure and applied mathematics. The book gives a comprehensive presentation of sub-Riemannian geometry and can be used by graduate students and experienced researchers. It could serve as a basis for various graduated courses: from an introductory course in Riemannian geometry to an advanced course in sub-Riemannian one, passing through elements of Hamiltonian dynamics, integrable systems and Lie theory.

A comprehensive introduction to sub-Riemannian geometry / Agrachev, A.; Barilari, D.; Boscain, U.. - 181:(2019), pp. 1-643.

### A comprehensive introduction to sub-Riemannian geometry

#### Abstract

Sub-Riemannian geometry is geometry of the world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. Mathematically this is a smooth manifold equipped with a noninvolutive vector distribution and an Euclidean structure on it. The unconstrained Riemannian world is an important special case. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with motivations and ramifications in several areas of pure and applied mathematics. The book gives a comprehensive presentation of sub-Riemannian geometry and can be used by graduate students and experienced researchers. It could serve as a basis for various graduated courses: from an introductory course in Riemannian geometry to an advanced course in sub-Riemannian one, passing through elements of Hamiltonian dynamics, integrable systems and Lie theory.
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2019
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11767/85326`