Overview

This book presents the most recent advances in complex Finsler geometry and related geometries: the geometry of complex Lagrange, Hamilton and Cartan Spaces. The last three spaces were initially introduced to and have been investigated by the author of the present volume over the past several years. This book will acquaint the reader with: - a survey of some basic results from complex manifolds and the complex vector bundles theory, - the geometry of holomorphic tangent bundles, - an analysis of the main results in complex Finsler geometry, - a study of the geometry of complex Lagrange and generalized Lagrange Spaces. Of special interest are their holomorphic subspaces, - the construction of the complex Hamilton geometry, - the complex Finsler vector bundles. Audience: Geometers, complex analysts, and physicists in quantum field theory and in theoretical mechanics will find this book of interest. The volume can be also used as a supplementary graduate text.

Full Product Details

Author:   Gheorghe Munteanu
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2004
Volume:   141
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9789048166145

ISBN 10:   9048166144
Pages:   228
Publication Date:   08 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Complex Manifolds.- 1.1 Rudiments of several complex variables.- 1.2 Complex and almost complex manifolds.- 1.3 Hermitian and Kählerian manifolds.- 2 Complex and holomorphic vector bundles.- 2.1 Complex vector bundles.- 2.2 Holomorphic vector bundles.- 2.3 Chern classes.- 2.4 Einstein-Hermitian vector bundles.- 3 The geometry of holomorphic tangent bundle.- 3.1 T?M manifold.- 3.2 N—complex linear connections on T?M.- 3.3 Metric structures on T?M.- 4 Complex Finsler spaces.- 4.1 Complex Finsler metrics.- 4.2 Chern-Finsler complex connection.- 4.3 Transformations of Finsler N - (c.l.c.).- 4.4 The Chern complex linear connection.- 4.5 Geodesic complex curves and holomorphic curvature.- 4.6 v-cohomology of complex Finsler manifolds.- 5 Complex Lagrange geometry.- 5.1 Complex Lagrange spaces.- 5.2 The generalized complex Lagrange spaces.- 5.3 Lagrange geometry via complex Lagrange geometry.- 5.4 Holomorphic subspaces of a complex Lagrange space.- 6 Hamilton and Cartan complex spaces.- 6.1 The geometry of T?*M bundle.- 6.2 N-complex linear connection on T?*M.- 6.3 Metric Hermitian structure on T?*M.- 6.4 Complex Hamilton space.- 6.5 Complex Cartan spaces.- 6.6 Complex Legendre transformation.- 6.7 ?-dual complex Lagrange-Hamilton spaces.- 6.8 ?-dual N - (c.l.c.).- 6.9 ?-dual complex Finsler-Cartan spaces.- 6.10 The ?-dual holomorphic sectional curvature.- 6.11 Recovering the real Hamilton geometry.- 6.12 Holomorphic subspaces of a complex Hamilton space.- 7 Complex Finsler vector bundles.- 7.1 The geometry of total space of a holomorphic vector bundle.- 7.2 Finsler structures and partial connections.

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