Résumé
In 1854, B Riemann introduced the notion of curvature for
spaces with a family of inner products. There was no
significant progress in the general case until 1918, when P
Finsler studied the variation problem in regular metric
spaces. Around 1926, L Berwald extended Riemann's notion of
curvature to regular metric spaces and introduced an
important non-Riemannian curvature using his connection for
regular metrics. Since then, Finsler geometry has developed
steadily. In his Paris address in 1900, D Hilbert
formulated 23 problems, the 4th and 23rd problems being in
Finsler's category. Finsler geometry has broader
applications in many areas of science and will continue to
develop through the efforts of many geometers around the
world.
Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.
Contents
- Finsler Spaces
- Finsler m Spaces
- Co-Area Formula
- Isoperimetric Inequalities
- Geodesics and Connection
- Riemann Curvature
- Non-Riemannian Curvatures
- Structure Equations
- Finsler Spaces of Constant Curvature
- Second Variation Formula
- Geodesics and Exponential Map
- Conjugate Radius and Injectivity Radius
- Basic Comparison Theorems
- Geometry of Hypersurfaces
- Geometry of Metric Spheres
- Volume Comparison Theorems
- Morse Theory of Loop Spaces
- Vanishing Theorems for Homotopy Groups
- Spaces of Finsler Spaces
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | World Scientific |
| Auteur(s) | Zhongmin Shen |
| Parution | 06/12/2001 |
| Nb. de pages | 306 |
| Format | 15,4 x 21,5 |
| Couverture | Broché |
| Poids | 445g |
| Intérieur | Noir et Blanc |
| EAN13 | 9789810245313 |
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