AL VANHECKE LIEVEN ET (EN) — RIEMANNIAN MANIFOLDS OF CONULLITY TWO

RIEMANNIAN MANIFOLDS OF CONULLITY TWO краткое содержание

RIEMANNIAN MANIFOLDS OF CONULLITY TWO - описание и краткое содержание, автор AL VANHECKE LIEVEN ET (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are “semi-symmetric spaces foliated by Euclidean leaves of codimension two” in the sense of Z I Szabó. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of “relative conullity two”. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or “almost rigid”. The unifying method is solving explicitly particular systems of nonlinear PDE.Contents:IntroductionDefinition of Semi-Symmetric Spaces and Early DevelopmentLocal Structure of Semi-Symmetric SpacesExplicit Treatment of Foliated Semi-Symmetric SpacesCurvature Homogeneous Semi-Symmetric SpacesAsymptotic Foliations and Algebraic RankThree-Dimensional Riemannian Manifolds of Conullity TwoAsymptotically Foliated Semi-Symmetric SpacesElliptic Semi-Symmetric SpacesComplete Foliated Semi-Symmetric SpacesApplication: Local Rigidity Problems for Hypersurfaces with Type Number Two in IR4Three-Dimensional Riemannian Manifolds of c-Conullity TwoMore about Curvature Homogeneous SpacesBiolographyIndexReadership: Mathematicians and mathematical physicists.Key Features:Interweaves historical vignettes, the profiles of scientists and the discussion of science into an interesting and attractive perspective on modern medicineContains many diagrams and figures that facilitate discussion, including many on original data setsAn original book, written by the initiator of many of the concepts in the field of fractal physiologyAccessible to students but of interest to experts