Geometry

Handbook of Differential Geometry

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 geometry and with research results (old geometry and recent). All chapters are written by experts in the area geometry 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 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 geometry and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics Copyright (C) Muze Inc. 2005. For personal use only. All rights reserved.
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Semi-Riemannian Geometry

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, geometry and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion geometry and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest. Copyright (C) Muze Inc. 2005. For personal use only. All rights reserved.
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Algebraic geometry and analytic geometry - In mathematics, algebraic geometry and analytic geometry are two closely related subjects. Where algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables.

Non-Euclidean geometry - The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines.

Birational geometry - In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension 2, the birational geometry of algebraic surfaces was largely worked out by the Italian school of algebraic geometry in the two decades on either side of the year 1900.

Absolute geometry - Absolute geometry is a geometry that does not assume the parallel postulate or any of its alternatives. Its theorems are therefore true in non-Euclidean geometries, such as hyperbolic geometry and elliptic geometry, as well as in Euclidean geometry.

geometry

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