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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