Keywords:
Geometry, Differential
;
Calculus of variations
;
Calculus of variations
;
Geometry, Differential
;
Geometry, Differential
;
Calculus of variations
;
Electronic books
;
Electronic books
Description / Table of Contents:
Tangent vector-vector field formalism -- Differential forms -- Specialization to euclidean spaces : differential manifolds -- Mappings, submanifolds, and the implicit function theorem -- Jacobi bracket and the lie theory of ordinary differential equations -- Frobenius complete integrability theorem -- Reduction of dimension when a lie algebra of vector fields leaves a vector-fields invariant -- Lie groups -- Classical mechanics of particles and continua -- Differential forms and variational problems -- Hamilton-Jacobi theory -- Extremal fields and sufficient conditions for a minimum -- Ordinary problems of the calculus of variations -- Groups of symmetries of variational problems : applications to mechanics -- Elliptic functions -- Accessibility problems for path systems -- Affine connections on differential manifolds -- Rinmannian affine connection and the first variation formula -- Hopf-Rinow theorem applications to the theory of covering spaces -- Second variation formula and Jacobi vector fields -- Sectional curvature and the elementary comparision theorems -- Submanifolds of Riemannian manifolds -- Groups of isometries -- Deformation of submanifolds in Riemannian spaces -- First-order invariants of submanifolds and convexity for affinely connected manifolds -- Affine groups of automorphisms, induced connections on submanifolds, projective changes of connection -- Laplace-Beltrami operator -- Characteristics and shock waves -- Morse index theorem -- Complex manifolds and their submanifolds -- Mechanics on Riemannian manifolds
Type of Medium:
Online Resource
Pages:
Online Ressource (vii, 440 pages)
Edition:
Online-Ausg.
ISBN:
0123421500
,
9780123421500
Series Statement:
Mathematics in Science and Engineering v. 49
URL:
http://www.sciencedirect.com/science/book/9780123421500
URL:
http://www.sciencedirect.com/science/bookseries/00765392/49
URL:
https://www.sciencedirect.com/science/bookseries/00765392/49
DDC:
516.36
Language:
English
Note:
Includes bibliographical references and index. - Print version record
,
Tangent vector-vector field formalismDifferential forms -- Specialization to euclidean spaces : differential manifolds -- Mappings, submanifolds, and the implicit function theorem -- Jacobi bracket and the lie theory of ordinary differential equations -- Frobenius complete integrability theorem -- Reduction of dimension when a lie algebra of vector fields leaves a vector-fields invariant -- Lie groups -- Classical mechanics of particles and continua -- Differential forms and variational problems -- Hamilton-Jacobi theory -- Extremal fields and sufficient conditions for a minimum -- Ordinary problems of the calculus of variations -- Groups of symmetries of variational problems : applications to mechanics -- Elliptic functions -- Accessibility problems for path systems -- Affine connections on differential manifolds -- Rinmannian affine connection and the first variation formula -- Hopf-Rinow theorem applications to the theory of covering spaces -- Second variation formula and Jacobi vector fields -- Sectional curvature and the elementary comparision theorems -- Submanifolds of Riemannian manifolds -- Groups of isometries -- Deformation of submanifolds in Riemannian spaces -- First-order invariants of submanifolds and convexity for affinely connected manifolds -- Affine groups of automorphisms, induced connections on submanifolds, projective changes of connection -- Laplace-Beltrami operator -- Characteristics and shock waves -- Morse index theorem -- Complex manifolds and their submanifolds -- Mechanics on Riemannian manifolds.
,
Tangent vector-vector field formalism -- Differential forms -- Specialization to euclidean spaces : differential manifolds -- Mappings, submanifolds, and the implicit function theorem -- Jacobi bracket and the lie theory of ordinary differential equations -- Frobenius complete integrability theorem -- Reduction of dimension when a lie algebra of vector fields leaves a vector-fields invariant -- Lie groups -- Classical mechanics of particles and continua -- Differential forms and variational problems -- Hamilton-Jacobi theory -- Extremal fields and sufficient conditions for a minimum -- Ordinary problems of the calculus of variations -- Groups of symmetries of variational problems : applications to mechanics -- Elliptic functions -- Accessibility problems for path systems -- Affine connections on differential manifolds -- Rinmannian affine connection and the first variation formula -- Hopf-Rinow theorem applications to the theory of covering spaces -- Second variation formula and Jacobi vector fields -- Sectional curvature and the elementary comparision theorems -- Submanifolds of Riemannian manifolds -- Groups of isometries -- Deformation of submanifolds in Riemannian spaces -- First-order invariants of submanifolds and convexity for affinely connected manifolds -- Affine groups of automorphisms, induced connections on submanifolds, projective changes of connection -- Laplace-Beltrami operator -- Characteristics and shock waves -- Morse index theorem -- Complex manifolds and their submanifolds -- Mechanics on Riemannian manifolds.
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