Finsler Metrics - A Global Approach

1. Front Matter

   Pages I-IX

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2. Real Finsler geometry

   • Marco Abate, Giorgio Patrizio

   Pages 1-62

3. Complex Finsler geometry

   • Marco Abate, Giorgio Patrizio

   Pages 63-125

4. Manifolds with constant holomorphic curvature

   • Marco Abate, Giorgio Patrizio

   Pages 127-170

5. Back Matter

   Pages 171-177

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Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.

• Complex analysis
• Finsler geometry
• Finsler metrics
• complex Finsler metrics
• complex Monge-Ampere equation
• complex geodesics
• curvature
• differential geometry
• intrinsic metrics
• manifold

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