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An introduction to Finsler geometry [[electronic resource] /] / Xiaohuan Mo
| An introduction to Finsler geometry [[electronic resource] /] / Xiaohuan Mo |
| Autore | Mo Xiao-huan |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina | 516.375 |
| Collana | Peking University series in mathematics |
| Soggetto topico |
Finsler spaces
Geometry, Riemannian Manifolds (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-92492-X
9786611924928 981-277-371-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; 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 Invariants4.1 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 Invariants7.1 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 tensor9.5 Harmonicity of the identity map; Bibliography; Index |
| Record Nr. | UNINA-9910453383203321 |
Mo Xiao-huan
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to Finsler geometry [[electronic resource] /] / Xiaohuan Mo
| An introduction to Finsler geometry [[electronic resource] /] / Xiaohuan Mo |
| Autore | Mo Xiao-huan |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina | 516.375 |
| Collana | Peking University series in mathematics |
| Soggetto topico |
Finsler spaces
Geometry, Riemannian Manifolds (Mathematics) |
| ISBN |
1-281-92492-X
9786611924928 981-277-371-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; 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 Invariants4.1 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 Invariants7.1 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 tensor9.5 Harmonicity of the identity map; Bibliography; Index |
| Record Nr. | UNINA-9910782317703321 |
|
Mo Xiao-huan
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to Finsler geometry / / Xiaohuan Mo
| An introduction to Finsler geometry / / Xiaohuan Mo |
| Autore | Mo Xiao-huan |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina | 516.375 |
| Collana | Peking University series in mathematics |
| Soggetto topico |
Finsler spaces
Geometry, Riemannian Manifolds (Mathematics) |
| ISBN |
1-281-92492-X
9786611924928 981-277-371-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; 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 Invariants4.1 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 Invariants7.1 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 tensor9.5 Harmonicity of the identity map; Bibliography; Index |
| Record Nr. | UNINA-9910824442403321 |
|
Mo Xiao-huan
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||