Screen LibraryAn introduction to Finsler geometry /
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Published: |
World Scientific,
|
| Publisher Address: | Singapore ; Hackensack, N.J. : |
| Publication Dates: | 2006. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Peking University series in mathematics ;
v. 1 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/6095#t=toc |
| Carrier Form: | 1 online resource (viii,120pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 117-118) and index. |
| ISBN: |
9812773711 (electronic bk.) 9789812773715 (electronic bk.) |
| CLC: | O186.14 |
| Contents: | 1. Finsler manifolds. 1.1. Historical remarks. 1.2. Finsler manifolds. 1.3. Basic examples. 1.4. Fundamental invariants. 1.5. Reversible Finsler structures -- 2. Geometric quantities on a Minkowski space. 2.1. The Cartan tensor. 2.2. The Cartan form and Deicke's theorem. 2.3. Distortion. 2.4. Finsler submanifolds. 2.5. Imbedding problem of submanifolds -- 3. Chern connection. 3.1. The adapted frame on a Finsler bundle. 3.2. Construction of Chern connection. 3.3. Properties of Chern connection. 3.4. Horizontal and vertical subbundles of SM -- 4. Covariant differentiation and second class of geometric invariants. 4.1. Horizontal and vertical covariant derivatives. 4.2. The covariant derivative along geodesic. 4.3. Landsberg curvature. 4.4. S-curvature -- 5. Riemann invariants and variations of arc length. 5.1. Curvatures of Chern connection. 5.2. Flag curvature. 5.3. The first variation of arc length. 5.4. The second variation of arc length -- 6. Geometry of projective sphere bundle. 6.1. Riemannian connection and curvature of projective sphere bundle. 6.2. Integrable condition of Finsler bundle. 6.3. Minimal condition of Finsler bundle -- 7. Relation among three classes of invariants. 7.1. The relation between Cartan tensor and flag curvature. 7.2. Ricci identities. 7.3. The relation between S-curvature and flag curvature. 7.4. Finsler manifolds with constant S-curvature -- 8. Finsler manifolds with scalar curvature. 8.1. Finsler manifolds with isotropic S-curvature. 8.2. Fundamental equation on Finsler manifolds with scalar curvature. 8.3. Finsler metrics with relatively isotropic mean Landsberg curvature -- 9. Harmonic maps from Finsler manifolds. 9.1. Some definitions and lemmas. 9.2. The first variation. 9.3. Composition properties. 9.4. The stress-energy tensor. 9.5. Harmonicity of the identity map. |