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  • Book
  • © 1994

Finsler Metrics - A Global Approach

with Applications to Geometric Function Theory

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

Part of the book sub series: Scuola Normale Superiore, Pisa (3265)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-IX
  2. Real Finsler geometry

    • Marco Abate, Giorgio Patrizio
    Pages 1-62
  3. Complex Finsler geometry

    • Marco Abate, Giorgio Patrizio
    Pages 63-125
  4. Manifolds with constant holomorphic curvature

    • Marco Abate, Giorgio Patrizio
    Pages 127-170
  5. Back Matter

    Pages 171-177

About this book

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

  • Book Title: Finsler Metrics - A Global Approach

  • Book Subtitle: with Applications to Geometric Function Theory

  • Authors: Marco Abate, Giorgio Patrizio

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073980

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58465-0Published: 26 October 1994

  • eBook ISBN: 978-3-540-48812-5Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 182

  • Topics: Functions of a Complex Variable, Analysis, Differential Geometry

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions