Riemannian Manifolds of Conullity Two

Riemannian Manifolds of Conullity Two
Author: Eric Boeckx
Publisher: World Scientific
Total Pages: 319
Release: 1996
Genre: Mathematics
ISBN: 981022768X

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 Szab¢. 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.

Riemannian Manifolds Of Conullity Two

Riemannian Manifolds Of Conullity Two
Author: Eric Boeckx
Publisher: World Scientific
Total Pages: 319
Release: 1996-11-09
Genre: Mathematics
ISBN: 9814498556

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.

Perspectives of Complex Analysis, Differential Geometry and Mathematical Physics

Perspectives of Complex Analysis, Differential Geometry and Mathematical Physics
Author: Stancho Dimiev
Publisher: World Scientific
Total Pages: 220
Release: 2001
Genre: Mathematics
ISBN: 9812810145

The Deligne-Simpson problem for zero index of rigidity / V.P. Rostov -- Theorems for extension on manifolds with almost complex structures / L.N. Apostolova, M.S. Marinov and K.P. Petrov -- The theorem on analytic representation on hypersurface with singularities / A.M. Kytmanov and S.G. Myslivets -- Pseudogroup structures on Spencer manifolds / S. Dimiev -- Type-changing transformations of Hurwitz pairs, quasiregular functions, and hyper Kahlerian holomorphic chains I / J. Lawrynowicz and L.M. Tovar -- Embedding of the moduli space of Riemann surfaces with Igeta structures into the Sato Grassmann manifold / Y. Hashimoto and K. Ohba -- On the quotient spaces of S2 x S2 under the natural action of subgroups of D4 / K. Kikuchi -- Existence of spin structures on cyclic branched covering spaces over four-manifolds / S. Nagami -- Length spectrum of geodesic spheres in rank one symmetric spaces / T. Adachi -- Grassmann geometry of 6-dimensional sphere, II / H. Hashimoto and K. Mashimo -- Hypersurfaces in Euclidean space which are one-parameter families of spheres / G. Ganchev and V. Mihova -- Hypersurfaces of conullity two in Euclidean space which are one-parameter systems of torses / G. Ganchev and V. Milousheva -- Real hypersurfaces of a Kaehler manifold (the sixteen classes) / G. Ganchev and M. Hristov -- Almost contact B-metric hypersurfaces of Kaehlerian manifolds with B-metric / M. Manev -- Projective formalism and some methods from algebraic geometry in the theory of gravitation / B.G. Dimitrov -- Geometry of manifolds and dark matter / I.B. Pestov -- Lagrangian fluid mechanics / S. Manoff -- Transformation of connectednesses / G. Zlatanov

Semiparallel Submanifolds in Space Forms

Semiparallel Submanifolds in Space Forms
Author: Ülo Lumiste
Publisher: Springer Science & Business Media
Total Pages: 306
Release: 2009-03-02
Genre: Mathematics
ISBN: 038749913X

Quite simply, this book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, detailing symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. The book then introduces semiparallel submanifolds and gives some characterizations for their class as well as several subclasses. The coverage moves on to discuss the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. With more than 40 published papers under his belt on the subject, Lumiste provides readers with the most authoritative treatment.

The Geometry Of Curvature Homogeneous Pseudo-riemannian Manifolds

The Geometry Of Curvature Homogeneous Pseudo-riemannian Manifolds
Author: Peter B Gilkey
Publisher: World Scientific
Total Pages: 389
Release: 2007-04-26
Genre: Mathematics
ISBN: 1908979275

Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory./a

Foliations on Riemannian Manifolds and Submanifolds

Foliations on Riemannian Manifolds and Submanifolds
Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
Total Pages: 296
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461242703

This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.