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

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.

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.