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Differential geometry and the calculus of variations /
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
Elsevier Science,
1968.
|
| Colección: | Mathematics in science and engineering ;
v. 49. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- 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.