Finsler Metrics—A Global Approach

with applications to geometric function theory

  • Authors
  • Marco Abate
  • Giorgio Patrizio

Part of the Lecture Notes in Mathematics book series (LNM, volume 1591)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Marco Abate, Giorgio Patrizio
    Pages 1-62
  3. Marco Abate, Giorgio Patrizio
    Pages 63-125
  4. Marco Abate, Giorgio Patrizio
    Pages 127-170
  5. Back Matter
    Pages 171-177

About this book

Introduction

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.

Keywords

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

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073980
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58465-0
  • Online ISBN 978-3-540-48812-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book