Sub-Riemannian geometry : general theory and examples / Ovidiu Calin, Der-chen Chang.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introductory chapter -- Basic properties -- Horizontal connectivity -- Hamilton-Jacobi theory -- The Hamiltonian formalism -- Lagrangian formalism -- Connections on Sub-Riemannian manifolds -- Gauss' theory of Sub-Riemannian manifolds -- Heisenberg manifolds -- Examples of Heisenberg manifolds -- Grushin manifolds -- Hörmander manifolds -- Appendices. Local nonsolvability ; Fiber bundles.

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.