Victor Guillemin 
Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2, 1 [PDF ebook] 

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.