Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Topological groups. Lie groups --- Functional analysis --- topologie (wiskunde) --- functies (wiskunde)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds.

Kleinian groups. --- Differentiable dynamical systems. --- Topological Groups. --- Differential equations, partial. --- Dynamical Systems and Ergodic Theory. --- Topological Groups, Lie Groups. --- Several Complex Variables and Analytic Spaces. --- Partial differential equations --- Groups, Topological --- Continuous groups --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- Topological groups. --- Lie groups. --- Functions of complex variables. --- Ergodic transformations --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Complex variables --- Elliptic functions --- Functions of real variables --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Differential geometry. Global analysis --- Differential topology --- Geometry --- Analytical spaces --- Ergodic theory. Information theory --- Mathematical analysis --- landmeetkunde --- analyse (wiskunde) --- differentiaal geometrie --- topologie --- informatietheorie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The fundamental ideas of the classical geometries are presented in a clear and elementary way, making them accessible to a wide audience, and relating them to more advanced topics in modern geometry, such as manifolds, Lie groups, the Gaussian curvature, group actions, and foliations. The book appeals to, and develops, the geometric intuition of the reader. The only prerequisites are calculus, linear algebra and basic analytic geometry. After studying the material, the reader will have a good understanding of basic geometry as well as a clear picture of the relations of this beautiful subject to other branches of mathematics. This is supported by more than 100 carefully chosen illustrations and a large number of exercises. While mainly addressed to students at advanced undergraduate level, the text can be of interest to anyone wanting to learn classical geometry.

Geometry --- geometrie --- 514.11 --- 514.12 --- 514.12 Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Euclidean and pseudo-Euclidean geometries. Analytic geometry --- 514.11 Elementary geometry, trigonometry, polygonometry --- Elementary geometry, trigonometry, polygonometry --- Mathematics --- Euclid's Elements --- Geometry. --- Mathematics. --- Math --- Science --- Mathematics, general.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ˜good' notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.

Differential geometry. Global analysis --- Differential topology --- Geometry --- Analytical spaces --- Ergodic theory. Information theory --- Mathematical analysis --- landmeetkunde --- analyse (wiskunde) --- differentiaal geometrie --- topologie --- informatietheorie