Leçons et applications de géométrie différentielle et de mécanique analytique / Y. Talpaert

The book is a comprehensive introduction to differential geometry, necessary to students and researchers interested in the applications of geometrical concepts and techniques to various fields of mathematics and physics. Here are presented, in a very clear and rigorous form, important notions and results concerning: differentiable manifolds, tangent and cotangent bundles, tensor fields and differential forms, linear connections, Riemannian and symplectic structures, Lie groups and algebras, etc. The material presented is then applied to the d'Alembert- Lagrange and Hamilton-Jacobi analytical mechanics. The exposition is completed with 126 solved exercises, that are very useful for a thorough study of the concepts being introduced and the corresponding techniques. (Zentralblatt)

Bibliogr. p. 459-460. Index