Sub-Riemannian Geometry
General Theory and Examples
Published on 20. April 2009
Book
Hardback
386 pages
978-0-521-89730-3 (ISBN)
Description
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.
Reviews / Votes
'... the authors give many interesting examples and applications ... this book will pose a good help to researchers and graduate students.' Zentralblatt MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
52 Line drawings, unspecified
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 25 mm
Weight
743 gr
ISBN-13
978-0-521-89730-3 (9780521897303)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
06/2013
1st Edition
Cambridge University Press
€102.99
Available for download
Persons
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.
Content
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.