000			02574nam a22003015i 4500
001			66647
005			20210416162102.0
010			_a978-3-7643-9900-9 _dcompra
090			_a66647
100			_a20150401d2009 k||y0pory50 ba
101			_aeng
102			_aCH
200			_aFamilies of conformally covariant differential operators, Q-curvature and holography _bDocumento electrónico _fAndreas Juhl
210			_aBasel _cBirkhäuser Basel _d2009
215			_aXIII, 490 p.
225			_aProgress in Mathematics
300			_aColocação: Online
303			_aThe central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Branson’s 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 Poincaré-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.
606			_935688 _aGeometria riemaniana
606			_918029 _aOperadores diferenciais
680			_aQA649
700			_939186 _aJuhl _bAndreas
801			_aPT _gRPC
856			_uhttp://dx.doi.org/10.1007/978-3-7643-9900-9
942			_2lcc _cF _n0