Differential geometry and the calculus of variations
By: [edited by] Robert Hermann
Series: Mathematics in Science and Engineering -- v. 49; Mathematics in science and engineering -- v. 49.
Publisher: Elsevier Science
Published: 1968
Place of publication: Amsterdam
Language: eng
Format: [electronic resource] /
Number of pages: 440
ISBN-13: 9780123421500
Subjects: Differential Geometry; Calculus of variations
Notes: Includes bibliographical references and index.

Description based on print version record.
Table of contents: title: Tangent vector-vector field formalism; title: Differential forms; title: Specialization to euclidean spaces : differential manifolds; title: Mappings, submanifolds, and the implicit function theorem; title: Jacobi bracket and the lie theory of ordinary differential equations; title: Frobenius complete integrability theorem; title: Reduction of dimension when a lie algebra of vector fields leaves a vector-fields invariant; title: Lie groups; title: Classical mechanics of particles and continua; title: Differential forms and variational problems; title: Hamilton-Jacobi theory; title: Extremal fields and sufficient conditions for a minimum; title: Ordinary problems of the calculus of variations; title: Groups of symmetries of variational problems : applications to mechanics; title: Elliptic functions; title: Accessibility problems for path systems; title: Affine connections on differential manifolds; title: Rinmannian affine connection and the first variation formula; title: Hopf-Rinow theorem applications to the theory of covering spaces; title: Second variation formula and Jacobi vector fields; title: Sectional curvature and the elementary comparision theorems; title: Submanifolds of Riemannian manifolds; title: Groups of isometries; title: Deformation of submanifolds in Riemannian spaces; title: First-order invariants of submanifolds and convexity for affinely connected manifolds; title: Affine groups of automorphisms, induced connections on submanifolds, projective changes of connection; title: Laplace-Beltrami operator; title: Characteristics and shock waves; title: Morse index theorem; title: Complex manifolds and their submanifolds; title: Mechanics on Riemannian manifolds.