Title: Finsler metrics-- a global approach
First published: 1994
Description: 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.
Subjects: Complex manifolds, Finsler spaces, Generalized spaces, Differential Geometry, Mathematics, Global analysis (Mathematics), Global differential geometry, Analysis
LC classification: QA3 .L28 no. 1591, QA689 .L28 no. 1591