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Mathematics - Analysis | Finsler Metrics - A Global Approach - with Applications to Geometric Function Theory

Finsler Metrics - A Global Approach

with Applications to Geometric Function Theory

Abate, Marco, Patrizio, Giorgio

1994, IX, 182 p.

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  • About this book

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.

Content Level » Research

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

Related subjects » Analysis - Geometry & Topology

Table of contents 

Real Finsler geometry.- Complex Finsler geometry.- Manifolds with constant holomorphic curvature.

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