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2012 | 10 | 5 | 1896-1913
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Free CR distributions

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EN
Abstrakty
EN
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in $\mathbb{C}^{n + n^2 } $ for all n > 1. In particular, we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
5
Strony
1896-1913
Opis fizyczny
Daty
wydano
2012-10-01
online
2012-07-24
Twórcy
autor
autor
Bibliografia
  • [1] Armstrong S., Free 3-distributions: holonomy, Fefferman constructions and dual distributions, preprint available at http://arxiv.org/abs/0708.3027
  • [2] Čap A., Correspondence spaces and twistor spaces for parabolic geometries, J. Reine Angew. Math., 2005, 582, 143–172
  • [3] Čap A., Slovák J., Parabolic Geometries I, Math. Surveys Monogr., 154, American Mathematical Society, Providence, 2009
  • [4] Doubrov B., Slovák J., Inclusions between parabolic geometries, Pure Appl. Math. Q., 2010, 6(3), Special Issue: In Honor of Joseph J.Kohn, Part 1, 755–780
  • [5] Ežov V.V., Schmalz G., Poincaré automorphisms for nondegenerate CR quadrics, Math. Ann., 1994, 298(1), 79–87 http://dx.doi.org/10.1007/BF01459726
  • [6] Schmalz G., Slovák J., The geometry of hyperbolic and elliptic CR-manifolds of codimension two, Asian J. Math., 2000, 4(3), 565–598
  • [7] Schmalz G., Slovák J., Addendum to ”The geometry of hyperbolic and elliptic CR-manifolds of codimension two”, Asian J. Math., 4, 565–598, 2000, Asian J. Math., 2003, 7(3), 303–306
  • [8] Šilhan J., A real analog of Kostant’s version of the Bott-Borel-Weil theorem, J. Lie Theory, 2004, 14(2), 481–499
  • [9] Tanaka N., On the equivalence problem associated with simple graded Lie algebras, Hokkaido Math. J., 1979, 8(1), 23–84
  • [10] Yamaguchi K., Differential systems associated with simple graded Lie algebras, In: Progress in Differential Geometry, Adv. Stud. Pure Math., 22, Mathematical Society of Japan, Tokyo, 1993, 413–494
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0090-y
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