EAN: 9780099571742

HENNING MANKELL - GEBRAUCHT THE FIFTH WOMAN KUR...

This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension
greater than or equal to 2. With natural properties of (general) translations and general
distances of X euclidean  hyperbolic translations and distances  respectively  are
characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied
(besides euclidean and hyperbolic geometry)  as well as geometries where Lorentz
transformations play the key role. The geometrical notions of this book are based on general
spaces X as described. This implies that also mathematicians who have not so far been
especially interested in geometry may study and understand great ideas of classical geometries
in modern and general contexts. Proofs of newer theorems  characterizing isometries and Lorentz
transformations under mild hypotheses are included  like for instance infinite dimensional
versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is
the dimension-free approach to important geometrical theories. Only prerequisites are basic
linear algebra and basic 2- and 3-dimensional real geometry. TOC:Preface.- Translation Groups.-
Euclidean and Hyperbolic Geometry.- Sphere Geometries of Möbius and Lie.- Lorentz
Transformations.- Bibliography.- Notation and Symbols.- Index.

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