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＜E-Book＞
Classical Geometries in Modern Contexts : Geometry of Real Inner Product Spaces / by Walter Benz

Edition	1st ed. 2005.
Publisher	Basel : Birkhäuser Basel : Imprint: Birkhäuser
Year	2005
Language	English
Size	XII, 244 p : online resource
Authors	*Benz, Walter author SpringerLink (Online service)
Subjects	LCSH:Geometry LCSH:Mathematical physics FREE:Geometry FREE:Mathematical Methods in Physics
Notes	Translation Groups -- Euclidean and Hyperbolic Geometry -- Sphere Geometries of Möbius and Lie -- Lorentz Transformations 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 and hyperbolic geometries 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 HTTP:URL=https://doi.org/10.1007/3-7643-7432-2

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