Finsler Metrics - A Global Approach

With Applications to Geometric Function Theory

By: Marco Abate, Giorgio Patrizio

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Paperback | 26 October 1994

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196 Pages

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22.86 x 15.88 x 1.27

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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, K¤hlerianity, geodesics, curvature. Finally global geometry and complex Monge-Amp¨re 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.

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Preface
Real Finsler geometry
Non linear connections	p. 3
Vertical connections	p. 15
Torsion and curvature	p. 19
The Cartan connection	p. 24
First and second variations	p. 32
The exponential map	p. 39
Jacobi fields and Auslander's theorems	p. 51
Complex Finsler geometry
Complex non-linear connections	p. 64
Complex vertical connections	p. 76
The Chern-Finsler connection	p. 84
Variations of the length integral	p. 96
Holomorphic curvature	p. 105
The Cartan connection vs. the Chern-Finsler connection	p. 111
Manifolds with constant holomorphic curvature
Geodesic complex curves	p. 128
Manifolds with constant nonpositive holomorphic curvature	p. 147
Characterization of C[superscript n] and of convex circular domains	p. 161
References	p. 171
List of symbols	p. 175
Index	p. 179
Table of Contents provided by Blackwell. All Rights Reserved.

Finsler Metrics - A Global Approach

With Applications to Geometric Function Theory

At a Glance

Paperback

Shipping

How to return your order

Defective items

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