000			03232nam a22004695i 4500
001			978-0-387-47322-2
003			DE-He213
005			20250710084001.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387473222 _a99780387473222
024	7		_a10.1007/978-0-387-47322-2 _2doi
082	0	4	_a516 _223
100	1		_aRatcliffe, John G. _eauthor.
245	1	0	_aFoundations of Hyperbolic Manifolds _h[recurso electrónico] / _cby John G. Ratcliffe.
250			_aSecond Edition.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXII, 783 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v149
505	0		_aEuclidean Geometry -- Spherical Geometry -- Hyperbolic Geometry -- Inversive Geometry -- Isometries of Hyperbolic Space -- Geometry of Discrete Groups -- Classical Discrete Groups -- Geometric Manifolds -- Geometric Surfaces -- Hyperbolic 3-Manifolds -- Hyperbolic n-Manifolds -- Geometrically Finite n-Manifolds -- Geometric Orbifolds.
520			_aThis book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem. The exposition if at the level of a second year graduate student with particular emphasis placed on readability and completeness of argument. After reading this book, the reader will have the necessary background to study the current research on hyperbolic manifolds. The second edition is a thorough revision of the first edition that embodies hundreds of changes, corrections, and additions, including over sixty new lemmas, theorems, and corollaries. The new main results are Schl\¬afli's differential formula and the $n$-dimensional Gauss-Bonnet theorem. John G. Ratcliffe is a Professor of Mathematics at Vanderbilt University.
650		0	_aMATHEMATICS.
650		0	_aGEOMETRY, ALGEBRAIC.
650		0	_aGEOMETRY.
650		0	_aTOPOLOGY.
650	1	4	_aMATHEMATICS.
650	2	4	_aGEOMETRY.
650	2	4	_aTOPOLOGY.
650	2	4	_aALGEBRAIC GEOMETRY.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387331973
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v149
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-47322-2 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57733 _d57733