Finsler Metrics - A Global Approach: with Applications to Geometric Function Theory / Edition 1

Finsler Metrics - A Global Approach: with Applications to Geometric Function Theory / Edition 1

by Marco Abate, Giorgio Patrizio
     
 

ISBN-10: 354058465X

ISBN-13: 9783540584650

Pub. Date: 11/29/1994

Publisher: Springer Berlin Heidelberg

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.

Overview

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.

Product Details

ISBN-13:
9783540584650
Publisher:
Springer Berlin Heidelberg
Publication date:
11/29/1994
Series:
Lecture Notes in Mathematics / Scuola Normale Superiore, Pisa (closed) Series, #1591
Edition description:
1994
Pages:
182
Product dimensions:
0.42(w) x 6.14(h) x 9.21(d)

Table of Contents

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

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