Finsler metrics-- a global approach
Subtitle: with applications to geometric function theory
By: Marco Abate, Giorgio Patrizio.
Contributors: Patrizio, Giorgio.
Series: Lecture notes in mathematics ;; 1591; Lecture notes in mathematics (Springer-Verlag) ;; 1591.
Publisher: Springer-Verlag
Published: 1994
Place of publication: Berlin; New York
Language: eng
Number of pages: 180
Subjects: Finsler spaces.; Complex manifolds.
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.
Notes: Includes bibliographical references (p. [171]-173) and index.