Pseudo-riemannian symmetric spaces

  • 108 Pages
  • 2.98 MB
  • English
American Mathematical Society , Providence, R.I
Symmetric spaces., Hermitian structures., Holonomy groups., Representations of algebras., Lie alge
StatementM. Cahen and M. Parker.
SeriesMemoirs of the American Society ; no. 229, Memoirs of the American Mathematical Society ;, no. 229.
ContributionsParker, M. 1939- joint author.
LC ClassificationsQA3 .A57 no. 229, QA649 .A57 no. 229
The Physical Object
Paginationiv, 108 p. ;
ID Numbers
Open LibraryOL4423037M
ISBN 100821822292
LC Control Number79027541

Aug 25,  · This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the by: Topics covered are: Classification of pseudo-Riemannian symmetric Pseudo-riemannian symmetric spaces book Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian Reviews: 1.

Dec 01,  · Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.

A publication of the European Mathematical Society This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field.

Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric space M to a triple consisting of: (i) a Lie algebra with involution (of dimension much smaller than the. (C) Pseudo-riemannian symmetric spaces are imbedded as minimal submanifolds of certain pseudo-riemannian hyperspheres in pseudo-euclidean spaces if and only if the associated orthogonal Jordan triple systems are non-degenerate Jordan triple systems (Theorem ).

Moreover we will list up pseudo-riemannian symmetric.R-spaces associated. classification of pseudo-Riemannian symmetric spaces of arbitrary signature, which is already too complicated a problem to expect a simple solution. Chapter 18 by Antonio Pseudo-riemannian symmetric spaces book.

Di Scala, Thomas Leistner and Thomas Neukirchner. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric by: In orderto understand non-reductive pseudo-Riemannian symmetric spaces one has to consider more general Lie algebras, which are, moreover, equipped with an invariant inner product.

The first two are Riemannian symmetric spaces, the third is a pseudo-Riemannian symmet- ric space. tion, to the Cartan-Killing metric on the space SU(2)/U(1) ∼ S2, the sphere.

On S2 the Cartan-Killing metric is negative-definite. We may just as well take it as positive definite. Abstract. We give a survey of the present knowledge regarding basic questions in harmonic analysis on pseudo-Riemannian symmetric spaces G /H, where G is a semisimple Lie group: The definition of the Fourier transform, the Plancherel formula, the inversion formula and the Paley-Wiener by: 4.

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Poincaré series for non-Riemannian locally symmetric spaces Fanny Kassela,1, Toshiyuki Kobayashib,2 aCNRS and Université Lille 1, Laboratoire Paul Painlevé, Villeneuve d’Ascq Cedex, France bKavli IPMU and Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo, Japan Abstract We initiate the spectral analysis of pseudo.

A pseudo-Riemannian manifold (,) is a differentiable manifold equipped with an everywhere non-degenerate, smooth, symmetric metric tensor. Such a metric is called a pseudo-Riemannian metric.

Applied to a vector field, the resulting scalar field value at any point of the manifold can be positive, negative or zero. ASTRAHANCEV Then the Μ. (ζ = 1, 2) are also symmetric spaces, of which one is flat, and the other is of corank 1. Let us introduce into the discussion certain objects which are.

Introduction --Pseudo-Riemannian and pseudo-Hermitian symmetric spaces --Weakly irreducible spaces on which the action of the holonomy group is neither semi-simple nor nilpotent --Structure of the spaces admitting a maximal parallel foliation with zero curvature --Structure of the [script]S-module [italic]Y --Construction of the admissible [script]S-module [italic]y[subscript lowercase Greek]Alpha.

Pseudo-Riemannian Symmetric Spaces: Uniform Realizations and Open Embeddings into Grassmanians a point of a symmetric space is represented by a pair of complementary linear subspaces V1, V2 in.

Space form problems on symmetric spaces. Chapter 8. Riemannian symmetric spaces ; Chapter 9. Space forms of irreducible symmetric spaces ; Chapter Locally symmetric spaces of non-negative curvature AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services Cited by: Introduction I.

Pseudo-Riemannian and pseudo-Hermitian symmetric spaces II. Weakly irreducible spaces on which the action of the holonomy group is neither semi-simple nor nilpotent III. Structure of the spaces admitting a maximal parallel foliation with zero curvature IV.

The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on.

a semisimple symmetric space X= G=Hby discrete subgroups of G acting properly discontinuously and freely on X(\discontinuous groups for ").Such quotients are called pseudo-Riemannian locally sym-metric spaces. They are complete (G;X)-manifolds in the sense of Ehresmann and Thurston, and they inherit a pseudo-Riemannian structure from X.

Any. A general name given to various types of spaces in differential geometry. A manifold with an affine connection is called a locally symmetric affine space if the torsion tensor and the covariant derivative of the curvature tensor vanish identically.; A (pseudo-) Riemannian manifold is called a locally symmetric (pseudo-) Riemannian space if the covariant derivative of its curvature tensor with [a1]: A.L.

Besse, "Einstein manifolds", Springer (). For any function, the orbital integrals of are the pseudo-radial functions denoted by and and defined by ∫ where is the measure induced by the metric on the pseudo-spheres centered at in, namely Let be a semisimple pseudo-Riemannian symmetric space whose metric is of signature and be a base-point Thibaut Grouy.

Pseudo-Riemannian Spaces The Levi-Civita Connection The Curvature Tensor An interactive textbook developed along the lines of S. Helgason's book would be an important homogeneous, in particular symmetric spaces.

Submanifolds of Homogeneous Spaces with Cartan Methods Here I have in mind less the general theory but the. Kengmana T.

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() Characters of the Discrete Series for Pseudo-Riemannian Symmetric Spaces. In: Trombi P.C. (eds) Representation Theory of Reductive Groups.

Progress in Mathematics, vol Cited by: 3. Home» MAA Publications» MAA Reviews» Handbook of Pseudo-Riemannian Geometry and Supersymmetry.

Handbook of Pseudo-Riemannian Geometry and Supersymmetry. Vicente Cortés, editor. Classification results for pseudo-Riemannian symmetric spaces; D. Alekseevsky -- Pseudo-Kähler and para-Kähler symmetric spaces.

A symmetric space is called pseudo-Riemannian, if each symmetry, i.e. each S(p), is an isometry. The classification of all four dimensional pseudo-Riemannian symmetric spaces (with signature 1, - 3) reduces thus to two steps: Find all Lie triple systems in Minkowski space and find all covering spaces which give the same Lie triple by: 2.

We provide examples of naturally reductive pseudo-Riemannian spaces, in particular an example of a naturally reductive pseudo-Riemannian 2-stepnilpotent Lie group (N,h,i N), such that h,i N is invariant under a left action and for which the center is degenerate.

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From now on, we restrict ourselves to the pseudo-Riemannian symmetric spaces G/H given in Sections 1 and 2. We keep to the notation used in Section 2 throughout the rest of this paper.

Note that the Laplacian P on G/H is G- invariant. Concerning a geodesic. The space-time world of special relativity theory is the Lorentz space: the four-dimensional pseudo-Euclidean vector space of index 1, and that of the general relativity theory is a 4-dimensional pseudo-Riemannian manifold of index 1.

Thus the Mathematica concepts contained in this notebook. Also, we give a number of examples of weakly symmetric pseudo-Riemannian manifolds, some mirroring the Riemannian case and some indicating the problems in extending Riemannian results to weakly symmetric pseudo-Riemannian spaces.

In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point. This can be made more precise, in either the language of Riemannian geometry or of Lie theory.This book is the sixth edition of the classic Spaces of Constant Curvature, first published inwith the previous (fifth) edition published in It illustrates the high degree of interplay between group theory and geometry.

The reader will benefit from the very concise treatments of Riemannian and pseudo-Riemannian manifolds and their curvatures, of the representation theory of finite.This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity.

The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential.