 Abate, Marco.
 Berlin ; New York : SpringerVerlag, 1995.
 Description
 Book — 180 p.
 Summary

Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduatelevel introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kahlerianity, geodesics, curvature. Finally global geometry and complex MongeAmpere 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.
(source: Nielsen Book Data)
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