An Introduction to Finsler Geometry

The following sections are included:

• Preface

• Contents

The following sections are included:

• Historical remarks

• Finsler manifolds

• Basic examples

• Fundamental invariants

• Reversible Finsler structures

The following sections are included:

• The Cartan tensor

• The Cartan form and Deicke's Theorem

• Distortion

• Finsler submanifolds

• Imbedding problem of submanifolds

The following sections are included:

• The adapted frame on a Finsler bundle

• Construction of Chern connection

• Properties of Chern connection

• Horizontal and vertical subbundles of SM

The following sections are included:

• Horizontal and vertical covariant derivatives

• The covariant derivative along geodesic

• Landsberg curvature

• S-curvature

The following sections are included:

• Curvatures of Chern connection

• Flag curvature

• The first variation of arc length

• The second variation of arc length

The following sections are included:

• Riemannian connection and curvature of projective sphere bundle

• Integrable condition of Finsler bundle

• Minimal condition of Finsler bundle

The following sections are included:

• The relation between Cartan tensor and flag curvature

• Ricci identities

• The relation between S-curvature and flag curvature

• Finsler manifolds with constant S-curvature

The following sections are included:

• Finsler manifolds with isotropic S-curvature

• Fundamental equation on Finsler manifolds with scalar curvature

• Finsler metrics with relatively isotropic mean Landsberg curvature

The following sections are included:

• Some definitions and lemmas

• The first variation

• Composition properties

• The stress-energy tensor

• Harmonicity of the identity map

The following sections are included:

• Bibliography

• Index