Jacques Franchi and Yves Le Jan The idea of this book is to
illustrate an interplay between distinct domains of mathematics.
Firstly, this book provides an introduction to hyperbolic
geometry, based on the Lorentz group PSO(1, d) and its Iwasawa
decomposition, commutation relations and Haar measure, and on
the hyperbolic Laplacian. The Lorentz group plays a role in
relativistic space–time analogous to rotations in Euclidean
space. Hyperbolic geometry is the geometry of the unit pseudo-
sphere. The boundary of hyperbolic space is defined as the set
of light rays. Special attention is given to the geodesic and
horocyclic flows ... Read more Oxford Scholarship Online offers
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