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001			292947
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007			cr nn 008mamaa
008			150903s2012 sz | o |||| 0|eng d
020			_a9783034804202 _99783034804202
024	7		_a10.1007/9783034804202 _2doi
035			_avtls000345313
039		9	_a201509030411 _bVLOAD _c201405050319 _dVLOAD _y201402061333 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA440-699
100	1		_aBenz, Walter. _eautor _9325143
245	1	0	_aClassical Geometries in Modern Contexts : _bGeometry of Real Inner Product Spaces Third Edition / _cby Walter Benz.
250			_a3rd ed. 2012.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2012.
300			_axvii, 309 páginas _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
500			_aSpringer eBooks
505	0		_aPreface -- 1 Translation Groups -- 2 Euclidean and Hyperbolic Geometry -- 3 Sphere Geometries of Möbius and Lie -- 4 Lorentz Transformations -- 5 ?–Projective Mappings, Isomorphism Theorems -- 6 Planes of Leibniz, Lines of Weierstrass, Varia -- A Notation and symbols -- B Bibliography -- Index.
520			_aThe focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Möbius and Lie as well as geometries where Lorentz transformations play the key role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as 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. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these same spaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz-Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result in this edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the geometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all x in X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for reading this book are basic linear algebra and basic 2- and 3-dimensional real geometry. This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in modern and general contexts.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783034804196
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-0348-0420-2 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c292947 _d292947