000			03765nam a22005175i 4500
003			DE-He213
005			20191014041153.0
007			cr nn 008mamaa
008			100301s2009 sz | s |||| 0|eng d
020	6	4	_a9783764399009 _9978-3-7643-9900-9
024	8	7	_a10.1007/978-3-7643-9900-9 _2doi
050	8	4	_aQA641-670
072	8	7	_aPBMP _2bicssc
072	8	7	_aMAT012030 _2bisacsh
082			_a516.36 _223
100	8	1	_aJuhl, Andreas. _eauthor. _9216908
245	9	7	_aFamilies of Conformally Covariant Differential Operators, Q-Curvature and Holography _h[electronic resource] / _cby Andreas Juhl.
001			000075442
300	6	4	_aXIII, 490 p. _bonline resource.
490	8	1	_aProgress in Mathematics ; _v275
505	8	0	_aSpaces, Actions, Representations and Curvature -- Conformally Covariant Powers of the Laplacian, Q-curvature and Scattering Theory -- Paneitz Operator and Paneitz Curvature -- Intertwining Families -- Conformally Covariant Families.
520	6	4	_aThe central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Bransons Q-curvature. It was introduced by Thomas Branson about 15 years ago in connection with an attempt to systematise the structure of conformal anomalies of determinants of conformally covariant differential operators on Riemannian manifolds. Since then, numerous relations of Q-curvature to other subjects have been discovered, and the comprehension of its geometric significance in four dimensions was substantially enhanced through the studies of higher analogues of the Yamabe problem. The book attempts to reveal some of the structural properties of Q-curvature in general dimensions. This is achieved by the development of a new framework for such studies. One of the main properties of Q-curvature is that its transformation law under conformal changes of the metric is governed by a remarkable linear differential operator: a conformally covariant higher order generalization of the conformal Laplacian. In the new approach, these operators and the associated Q-curvatures are regarded as derived quantities of certain conformally covariant families of differential operators which are naturally associated to hypersurfaces in Riemannian manifolds. This method is at the cutting edge of several central developments in conformal differential geometry in the last two decades such as Fefferman-Graham ambient metrics, spectral theory on PoincarȨ-Einstein spaces, tractor calculus, and Cartan geometry. In addition, the present theory is strongly inspired by the realization of the idea of holography in the AdS/CFT-duality. This motivates the term holographic descriptions of Q-curvature.
650	8	0	_aMathematics. _98571
650	8	0	_aTopological Groups. _99529
650	8	0	_aGlobal analysis. _917903
650	8	0	_aGlobal differential geometry. _99530
650	8	0	_aMathematical physics. _99251
650			_aMathematics. _98571
650			_aDifferential Geometry. _99532
650			_aTopological Groups, Lie Groups. _99531
650			_aGlobal Analysis and Analysis on Manifolds. _917904
650			_aMathematical Methods in Physics. _99252
710	8	2	_aSpringerLink (Online service) _9216909
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783764398996
830	8	0	_aProgress in Mathematics ; _v275 _9216910
856			_uhttp://dx.doi.org/10.1007/978-3-7643-9900-9 _zde clik aquí para ver el libro electrónico
264	8	1	_aBasel : _bBirkhuser Basel, _c2009.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
912	6	4	_aZDB-2-SMA
999			_c75172 _d75172
942			_c05