Handbook of Differential GeometryFranki J.E. Dillen, Leopold C.A. Verstraelen 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, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research. Extensive bibliography. Dealing with a diverse range of areas. Starting from the basics |
Contents
| 35 | |
Symplectic Geometry | 79 |
Metric Riemannian Geometry | 189 |
Contact Geometry | 315 |
Complex Differential Geometry | 383 |
Compendium on the Geometry of Lagrange Spaces | 437 |
Certain Actual Topics on Modern Lorentzian Geometry | 513 |
| 547 | |
| 555 | |
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Common terms and phrases
3-manifolds Alexandrov space algebra Amer assume canonical codimension cohomology compact manifold complex manifold complex structure contact manifold contact structure convex coordinates curve defined DEFINITION denote diffeomorphism Differential Geom dimension embedding equations example exists feuilletages fiber finite Finsler manifolds Finsler metric Finsler spaces foliation function geodesic geometry given global Gromov Gromov–Hausdorff Hamiltonian Hausdorff Hence holomorphic homotopy implies integral invariant isometric isomorphism isotopy Kaehler manifold Kähler Lagrange space Lagrangian Legendrian Lemma Lie group linear Lorentzian manifold Math moment map n-dimensional N-linear neighborhood nonlinear connection oriented proof of Theorem Proposition prove remark respect Ricci curvature Riemannian manifold Riemannian metric satisfies sectional curvature smooth sphere submanifold subspace surface symplectic form symplectic manifold symplectomorphism tangent tensor timelike Topology transverse vector bundle vector field vector space zero
References to this book
Recent Advances in Riemannian and Lorentzian Geometries Krishan L. Duggal,Ramesh Sharma No preview available - 2003 |