Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121

Princeton University Press, 2 mrt. 2016 - 240 pagina's

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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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

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