Author | Abate, Marco. author |
---|---|

Title | Finsler Metricsโ{128}{148}A Global Approach [electronic resource] : with applications to geometric function theory / by Marco Abate, Giorgio Patrizio |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1994 |

Connect to | http://dx.doi.org/10.1007/BFb0073980 |

Descript | IX, 182 p. online resource |

SUMMARY

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

CONTENT

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