Sub-Riemannian Geometry: General Theory and Examples

by Ovidiu Calin, Der-Chen Chang

Overview

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.

Product Details

ISBN-13:	9780521897303
Publisher:	Cambridge University Press
Publication date:	04/20/2009
Series:	Encyclopedia of Mathematics and its Applications , #126
Pages:	386
Product dimensions:	6.10(w) x 9.30(h) x 1.30(d)

About the Author

Ovidiu Calin is an Associate Professor of Mathematics at Eastern Michigan University and a former Visiting Assistant Professor at the University of Notre Dame. He received his Ph.D. in geometric analysis from the University of Toronto in 2000. He has written several monographs and numerous research papers in the field of geometric analysis and has delivered research lectures in several universities in North America, Asia, the Middle East, and Eastern Europe.

Der-Chen Chang is Professor of Mathematics at Georgetown University. He is a previous Associate Professor at the University of Maryland and a Visiting Professor at the Academia Sinica, among other institutions. He received his Ph.D. in Fourier analysis from Princeton University in 1987 and has authored several monographs and numerous research papers in the field of geometric analysis, several complex variables, and Fourier analysis.

Table of Contents

Part I. General Theory: 1. Introductory chapter; 2. Basic properties; 3. Horizontal connectivity; 4. Hamilton-Jacobi theory; 5. Hamiltonian formalism; 6. Lagrangian formalism; 7. Connections on sub-Riemannian manifolds; 8. Gauss' theory of sub-Riemannian manifolds; Part II. Examples and Applications: 9. Heisenberg manifolds; 10. Examples of Heisenberg manifolds; 11. Grushin manifolds; 12. Hormander manifolds; Appendix A: local non-solvability; Appendix B: fibre bundles.

Editorial Reviews

'… the authors give many interesting examples and applications … this book will pose a good help to researchers and graduate students.' Zentralblatt MATH

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