media archive
Center & Programs Conferences Workshop on Flag Domains and Cycle Spaces
Loading the player ...
Non-degeneracy in CR Geometry
SPEAKER  |  Curtis Porter
INSTITUTE  |  
DATE  |  May 25(Thu), 2017
TIME  |  15:20
PLACE  |  1503
Keyword  |  
Download  |  
ABSTRACT  |  Orbits of real forms in complex flag manifolds often have interesting CR structures. These homogeneous spaces are known in some cases to be the "flat models" of a certain CR structure in the same sense that Euclidean vector spaces are the flat models of Riemannian geometry. In characterizing CR manifolds $M$, a central role is played by the Levi form $L$, which measures the failure of the CR bundle to be integrable, so that when $L$ has a nontrivial kernel of constant rank, $M$ is foliated by complex manifolds. If the local transverse structure to this foliation still determines a CR manifold $N$, $M$ is called straightenable, and the Tanaka-Chern-Moser classification of CR hypersurfaces with nondegenerate Levi form can be applied to $N$. It remains to classify those $M$ for which $L$ is degenerate and no such straightening exists. This was accomplished in dimension 5 by Ebenfelt, Isaev-Zaitzev, Medori-Spiro, and Pocchiola. I will discuss their results as well as my work (joint with Igor Zelenko) modifying Tanaka's prolongation procedure to treat the equivalence problem in arbitrary dimension, paying particular attention to the flat models.
  • Three Constructions ...
    Mark Green
    May 26(Fri), 2017
  • Hodge Theory and Mod...
    Phillip Griffiths
    May 26(Fri), 2017
  • Bi-algebraic geometr...
    Bruno Klingler
    May 25(Thu), 2017
  • Non-degeneracy in CR...
    Curtis Porter
    May 25(Thu), 2017
  • Differential geometr...
    Gregory Pearlstein
    May 25(Thu), 2017
  • Admissible nilpotent...
    Matt Kerr
    May 25(Thu), 2017
  • Admissible nilpotent...
    Matt Kerr
    May 24(Wed), 2017
  • Bi-algebraic geometr...
    Bruno Klingler
    May 24(Wed), 2017
  • Infinite Dimensional...
    Joseph A. Wolf
    May 24(Wed), 2017
  • On the intersection ...
    Ana-Maria Brecan
    May 24(Wed), 2017
  • Recognizing symplect...
    Jun-Muk Hwang
    May 23(Tue), 2017
  • Quantum K-theory of ...
    Nicolas Perrin
    May 23(Tue), 2017
  • The Riemann-Hilbert ...
    Bong H. Lian
    May 23(Tue), 2017
  • The Riemann-Hilbert ...
    Bong H. Lian
    May 23(Tue), 2017
  • Sub-VMRT structures ...
    Ngaiming Mok
    May 22(Mon), 2017
  • On cycle spaces of f...
    Sui-Chung Ng
    May 22(Mon), 2017
  • Sub-VMRT structures ...
    Ngaiming Mok
    May 22(Mon), 2017