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AuthorAbate, Marco. author
TitleFinsler Metricsโ{128}{148}A Global Approach [electronic resource] : with applications to geometric function theory / by Marco Abate, Giorgio Patrizio
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1994
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Descript IX, 182 p. online resource


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, Kรคhlerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampรจre 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


Real Finsler geometry -- Complex Finsler geometry -- Manifolds with constant holomorphic curvature

Mathematics Mathematical analysis Analysis (Mathematics) Functions of complex variables Differential geometry Mathematics Functions of a Complex Variable Analysis Differential Geometry


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