Finsler Metrics—A Global Approach
Abate, Marco.
Finsler Metrics—A Global Approach with applications to geometric function theory / [electronic resource] : by Marco Abate, Giorgio Patrizio. - IX, 182 p. online resource. - Scuola Normale Superiore, Pisa ; 1591 . - Scuola Normale Superiore, Pisa ; 1591 .
Real Finsler geometry -- Complex Finsler geometry -- Manifolds with constant holomorphic curvature.
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.
9783540488125
10.1007/BFb0073980 doi
Functions of complex variables.
Global analysis (Mathematics).
Global differential geometry.
Functions of a Complex Variable.
Analysis.
Differential Geometry.
QA331-355
515.9
Finsler Metrics—A Global Approach with applications to geometric function theory / [electronic resource] : by Marco Abate, Giorgio Patrizio. - IX, 182 p. online resource. - Scuola Normale Superiore, Pisa ; 1591 . - Scuola Normale Superiore, Pisa ; 1591 .
Real Finsler geometry -- Complex Finsler geometry -- Manifolds with constant holomorphic curvature.
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.
9783540488125
10.1007/BFb0073980 doi
Functions of complex variables.
Global analysis (Mathematics).
Global differential geometry.
Functions of a Complex Variable.
Analysis.
Differential Geometry.
QA331-355
515.9