06265nam 22017895 450 991015474690332120190708092533.01-4008-8241-910.1515/9781400882410(CKB)3710000000627786(SSID)ssj0001651256(PQKBManifestationID)16425852(PQKBTitleCode)TC0001651256(PQKBWorkID)12623624(PQKB)11346273(MiAaPQ)EBC4738718(DE-B1597)468030(OCoLC)979580918(DE-B1597)9781400882410(EXLCZ)99371000000062778620190708d2016 fg engurcnu||||||||txtccrCosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 /Victor GuilleminPrinceton, NJ : Princeton University Press, [2016]©19891 online resource (236 pages) illustrationsAnnals of Mathematics Studies ;352Bibliographic Level Mode of Issuance: Monograph0-691-08514-5 0-691-08513-7 Includes bibliographical references.Frontmatter -- Contents -- Foreword -- Part I. A relativistic approach to Zoll phenomena -- Part II. The general theory of Zollfrei deformations -- Part III. Zollfrei deformations of M2,1 -- Part IV. The generalized x-ray transform -- Part V. The Floquet theory -- BibliographyThe subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "Floquet operator," invented by Paneitz and Segal.Annals of mathematics studies ;no. 121.CosmologyMathematical modelsGeometry, DifferentialLorentz transformationsAutomorphism.Bijection.C0.Canonical form.Canonical transformation.Cauchy distribution.Causal structure.Cayley transform.Codimension.Cohomology.Cokernel.Compactification (mathematics).Complexification (Lie group).Computation.Conformal geometry.Conformal map.Conformal symmetry.Connected sum.Contact geometry.Corank.Covariant derivative.Covering space.Deformation theory.Diagram (category theory).Diffeomorphism.Differentiable manifold.Differential operator.Dimension (vector space).Einstein field equations.Equation.Euler characteristic.Existential quantification.Fiber bundle.Fibration.Floquet theory.Four-dimensional space.Fourier integral operator.Fourier transform.Fundamental group.Geodesic.Hamilton–Jacobi equation.Hilbert space.Holomorphic function.Holomorphic vector bundle.Hyperfunction.Hypersurface.Integral curve.Integral geometry.Integral transform.Intersection (set theory).Invertible matrix.K-finite.Lagrangian (field theory).Lie algebra.Light cone.Linear map.Manifold.Maxima and minima.Minkowski space.Module (mathematics).Notation.One-parameter group.Parametrix.Parametrization.Principal bundle.Product metric.Pseudo-differential operator.Quadratic equation.Quadratic form.Quadric.Radon transform.Riemann surface.Riemannian manifold.Seifert fiber space.Sheaf (mathematics).Siegel domain.Simply connected space.Submanifold.Submersion (mathematics).Support (mathematics).Surjective function.Symplectic manifold.Symplectic vector space.Symplectomorphism.Tangent space.Tautology (logic).Tensor product.Theorem.Topological space.Topology.Two-dimensional space.Unit vector.Universal enveloping algebra.Variable (mathematics).Vector bundle.Vector field.Vector space.Verma module.Volume form.X-ray transform.CosmologyMathematical models.Geometry, Differential.Lorentz transformations.523.1/072/4Guillemin Victor, 40563DE-B1597DE-B1597BOOK9910154746903321Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 1212788032UNINA