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Sub-Riemannian Geometry: General Theory and Examples: Encyclopedia of Mathematics and its Applications, cartea 126

Autor Ovidiu Calin, Der-Chen Chang
en Limba Engleză Hardback – 19 apr 2009
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.
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Specificații

ISBN-13: 9780521897303
ISBN-10: 0521897300
Pagini: 386
Ilustrații: 52 b/w illus.
Dimensiuni: 156 x 234 x 22 mm
Greutate: 0.68 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Encyclopedia of Mathematics and its Applications

Locul publicării:New York, United States

Cuprins

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.

Recenzii

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

Notă biografică


Descriere

A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.