UID:
almahu_9947367653402882
Format:
1 online resource (575 p.)
ISBN:
1-280-63113-9
,
9786610631131
,
0-08-046120-4
Series Statement:
Handbook of differential geometry ; 2
Content:
In the series of volumes which together will constitute the ""Handbook of Differential Geometry"" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, co
Note:
Description based upon print version of record.
,
Cover; Contents; Preface; List of Contributors; Contents of Volume I; Some Problems on Finsler Geometry; Introduction; Preliminaries; Volume and area in Finsler spaces; Unit spheres in Minkowski spaces; Symplectic equivalence of Finsler manifolds; Around Hilbert's fourth problem; Closed geodesics; Differential invariants of Finsler surfaces; References; Foliations; Foreword; Definitions and examples; Transverse structures; Codimension one foliations; Gamma-structures; The leaf space; Characteristic classes; Basic global analysis; Deformation theory of foliations; Some other themes; References
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Symplectic GeometryIntroduction; Symplectic manifolds; Lagrangian submanifolds; Complex structures; Symplectic geography; Hamiltonian geometry; Symplectic reduction; References; Metric Riemannian Geometry; Introduction; Sphere theorems; Finiteness theorems and Gromov-Hausdorff distance; Geodesic coordinate, injectivity radius, comparison theorems and sphere theorem; Packing and precompactness theorem; Construction of homeomorphism by isotopy theory; Harmonic coordinate and its application; Center of mass technique; Embedding Riemannian manifolds by distance function; Almost flat manifold
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Collapsing Riemannian manifolds-ICollapsing Riemannian manifolds-II; Collapsing Riemannian manifolds-III; Morse theory of distance function; Finiteness theorem by Morse theory; Soul theorem and splitting theorem; Alexandrov space-I; Alexandrov space-II; First Betti number and fundamental group; Hausdorff convergence of Einstein manifolds; Sphere theorem and L2 comparison theorem; Hausdorff convergence and Ricci curvature-I; Hausdorff convergence and Ricci curvature-II; References; Contact Geometry; Introduction; Contact manifolds; Contact structures on 3-manifolds; A guide to the literature
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ReferencesComplex Differential Geometry; Introduction; Complex manifolds; Almost complex structures; Dolbeault Lemma; Kaehler manifolds; Complex space forms; Laplace-Beltrami operator on a Hermitian manifold; Harmonic differential forms on Kaehler manifolds; Applications; Chern classes; Deformation of complex structures; References; Compendium on the Geometry of Lagrange Spaces; Introduction; Tangent bundle; Lagrange spaces; Finsler spaces; The geometry of T(k)M; Lagrange spaces of higher order; References; Certain Actual Topics on Modern Lorentzian Geometry; Preface
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Some aspects on the topology of Lorentzian manifoldsGeodesics and completeness; Curvature of Lorentzian manifolds; The Bochner technique on Lorentzian manifolds; References; Author Index; Subject Index
,
English
Additional Edition:
ISBN 0-444-52052-X
Language:
English
