000 02846nam a22004335i 4500
001 978-3-7643-9909-2
003 DE-He213
005 20140220084552.0
007 cr nn 008mamaa
008 110128s2010 sz | s |||| 0|eng d
020 _a9783764399092
_9978-3-7643-9909-2
024 7 _a10.1007/978-3-7643-9909-2
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aBaum, Helga.
_eauthor.
245 1 0 _aConformal Differential Geometry
_h[electronic resource] :
_bQ-Curvature and Conformal Holonomy /
_cby Helga Baum, Andreas Juhl.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2010.
300 _aX, 152 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOberwolfach Seminars ;
_v40
520 _aConformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of conformally covariant operators are the Yamabe, the Paneitz, the Dirac and the twistor operator. These operators are intimely connected with the notion of Branson’s Q-curvature. The aim of these lectures is to present the basic ideas and some of the recent developments around Q -curvature and conformal holonomy. The part on Q -curvature starts with a discussion of its origins and its relevance in geometry and spectral theory. The following lectures describe the fundamental relation between Q -curvature and scattering theory on asymptotically hyperbolic manifolds. Building on this, they introduce the recent concept of Q -curvature polynomials and use these to reveal the recursive structure of Q -curvatures. The part on conformal holonomy starts with an introduction to Cartan connections and its holonomy groups. Then we define holonomy groups of conformal manifolds, discuss its relation to Einstein metrics and recent classification results in Riemannian and Lorentzian signature. In particular, we explain the connection between conformal holonomy and conformal Killing forms and spinors, and describe Fefferman metrics in CR geometry as Lorentzian manifold with conformal holonomy SU(1,m).
650 0 _aMathematics.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
700 1 _aJuhl, Andreas.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764399085
830 0 _aOberwolfach Seminars ;
_v40
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7643-9909-2
912 _aZDB-2-SMA
999 _c112989
_d112989