Finsler Metrics - A Global Approach: with Applications to Geometric Function Theory (Lecture Notes in Mathematics (1591))

Abate, Marco, Patrizio, Giorgio

ISBN 10: 354058465X / ISBN 13: 9783540584650

Published by Springer, 1994

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Bibliographic Details

• Title: Finsler Metrics - A Global Approach: with Applications to Geometric Function Theory (Lecture Notes in Mathematics (1591))
• Publisher: Springer
• Publication Date: 1994
• Language: English
• ISBN 10: 354058465X
• ISBN 13: 9783540584650
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

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.