by Xiaohuan Mo (Peking University, China)

This introductory book uses the moving frame as a tool and develops Finsler geometry on the basis of the Chern connection and the projective sphere bundle. It systematically introduces three classes of geometrical invariants on Finsler manifolds and their intrinsic relations, analyzes local and global results from classic and modern Finsler geometry, and gives non-trivial examples of Finsler manifolds satisfying different curvature conditions.

• Finsler Manifolds
• Geometric Quantities on a Minkowski Space
• Chern Connection
• Covariant Differentiation and Second Class of Geometric Invariants
• Riemann Invariants and Variations of Arc Length
• Geometry of Projective Sphere Bundle
• Relation Among Three Classes of Invariants
• Finsler Manifolds with Scalar Curvature
• Harmonic Maps from Finsler Manifolds