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＜E-Book＞
Finsler Metrics - A Global Approach : with Applications to Geometric Function Theory / by Marco Abate, Giorgio Patrizio
(Scuola Normale Superiore, Pisa ; 1591)

Edition	1st ed. 1994.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1994
Size	IX, 182 p : online resource
Authors	*Abate, Marco author Patrizio, Giorgio author SpringerLink (Online service)
Subjects	LCSH:Functions of complex variables LCSH:Mathematical analysis LCSH:Geometry, Differential FREE:Functions of a Complex Variable FREE:Analysis FREE:Differential Geometry
Notes	Real Finsler geometry -- Complex Finsler geometry -- Manifolds with constant holomorphic curvature 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 HTTP:URL=https://doi.org/10.1007/BFb0073980

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