Leseprobe
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Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121
Victor Guillemin
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
The 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.
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Quadric, Seifert fiber space, X-ray transform, Covering space, Holomorphic function, Causal structure, Maxima and minima, Diagram (category theory), Tautology (logic), Deformation theory, Module (mathematics), Symplectomorphism, Canonical form, Siegel domain, Cohomology, Lie algebra, Cauchy distribution, Equation, Existential quantification, Corank, Parametrix, Submersion (mathematics), Dimension (vector space), Tensor product, Connected sum, Hypersurface, Integral geometry, Diffeomorphism, Einstein field equations, Theorem, Intersection (set theory), Variable (mathematics), Linear map, Tangent space, C0, Conformal geometry, Fourier integral operator, Contact geometry, Symplectic manifold, Vector field, Product metric, Quadratic equation, Riemann surface, Conformal map, Geodesic, Quadratic form, Symplectic vector space, Minkowski space, Canonical transformation, Automorphism, Volume form, Submanifold, Verma module, Two-dimensional space, Universal enveloping algebra, Radon transform, Pseudo-differential operator, Vector bundle, Compactification (mathematics), Hilbert space, Fibration, Integral transform, Integral curve, Lagrangian (field theory), Four-dimensional space, Hamilton–Jacobi equation, Codimension, Riemannian manifold, Floquet theory, Sheaf (mathematics)