Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121The 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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Inhoudsopgave
PART I A relativistic approach to Zoll phenomena 13 | |
PART II The general theory of Zollfrei deformations 48 | |
PART III Zollfrei deformations of M21 913 | |
PART IV The generalized xray transform 1417 | |
PART V The Floquet theory 1819 | |
Veelvoorkomende woorden en zinsdelen
associated assume bundle canonical canonical transformation causal clear close compact compose compute cone conformal conformally invariant consider construction coordinates corresponding cotangent cover curve cyclic defined definition deformations denote density depending smoothly described diagonal diagram diffeomorphism differential dimension double fibration easy Einstein equation estimates examples exists expression fact fiber figure fixed Floquet fold formula geodesics geometry given gives hand hence holomorphic homogeneous function homogeneous of degree identified identity infinitesmal integral integral operator interesting intersection Lagrangian light Lorentz metric manifold means microlocal Moreover normal Notice null-geodesics obtain one-form particular periodic problem projective Proof Proposition prove pseudodifferential operator quadratic respect restriction satisfies smooth smooth function solutions space standard structure submanifold subspaces Suppose symbol symplectic tensor Theorem tion transform unique vanishes vector field zero Zollfrei metrics
Bibliografische gegevens
| Titel | Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 Annals of Mathematics Studies |
| Auteur | Victor Guillemin |
| Uitgever | Princeton University Press, 2016 |
| ISBN | 1400882419, 9781400882410 |
| Lengte | 240 pagina's |
| Citatie exporteren | BiBTeX EndNote RefMan |