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

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. CONTENTS FOREWORD PART I. A relativistic approach to Zoll phenomena (§§1-3) PART II. The general theory of Zollfrei deformations (§§4-8) PART III. Zollfrei deformations of M2,1 (§§9-13) PART IV. The generalized x-ray transform (§§14-17) PART V. The Floquet theory (§§18-19) BIBLIOGRAPHY