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Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-27 /
Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
River Edge, NJ :
World Scientific,
©2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Machine generated contents note: Method of Moving Frames
- Theory of Pfaffian Forms
- Integration of Systems of Pfaffian Differential Equations
- Generalization
- Existence Theorem for a Family of Frames with Given Infinitesimal Components w[superscript i] and w[superscript i][subscript j]
- Fundamental Theorem of Metric Geometry
- Vector Analysis in an n-Dimensional Euclidean Space
- Fundamental Principles of Tensor Algebra
- Tensor Analysis
- Notion of a Manifold
- Locally Euclidean Riemannian Manifolds
- Euclidean Space Tangent at a Point
- Osculating Euclidean Space
- Euclidean Space of Conjugacy Along a Line
- Space with a Euclidean Connection
- Riemannian Curvature of a Manifold
- Spaces of Constant Curvature
- Geometric Construction of a Space of Constant Curvature
- Variational Problems for Geodesics
- Distribution of Geodesics Near a Given Geodesic
- Geodesic Surfaces
- Lines in a Riemannian Manifold
- Surfaces in a Three-Dimensional Riemannian Manifold
- Forms of Laguerre and Darboux.