/lhjurxsvwuxfwxuhvrqdxwrprusklvpjurxsvriuhdodqdo\wlf &5pdqlirogv Lie Group Structures on Automorphism Groups of Real-analytic Cr Manifolds

نویسنده

  • DMITRI ZAITSEV
چکیده

Given any real-analytic CR manifold M, we provide general conditions on M guaranteeing that the group of all its global real-analytic CR automorphisms AutCR (M) is a Lie group (in an appropriate topology). In particular, we obtain a Lie group structure for AutCR (M) when M is an arbitrary compact real-analytic hypersurface embedded in some Stein manifold.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

CR-manifolds of dimension 5: A Lie algebra approach

We study real-analytic Levi degenerate hypersurfaces M in complex manifolds of dimension 3, for which the CR-automorphism group Aut(M) is a real Lie group acting transitively on M . We provide large classes of examples for such M , compute the corresponding groups Aut(M) and determine the maximal subsets of M that cannot be separated by global continuous CR-functions. It turns out that all our ...

متن کامل

Ju n 20 09 Regularization of Local CR - Automorphisms of Real - Analytic CR - Manifolds ∗

Let M be a connected generic real-analytic CR-submanifold of a finite-dimensional complex vector space E. Suppose that for every a ∈ M the Lie algebra hol(M,a) of germs of all infinitesimal real-analytic CR-automorphisms of M at a is finitedimensional and its complexification contains all constant vector fields α∂/∂z , α ∈ E, and the Euler vector field z ∂/∂z . Under these assumptions we show t...

متن کامل

Complete hyperbolic Stein manifolds with prescribed automorphism groups

It is well known that the automorphism group of a hyperbolic manifold is a Lie group. Conversely, it is interesting to see whether or not any Lie group can be prescribed as the automorphism group of a certain complex manifold. When the Lie group G is compact and connected, this problem has been completely solved by Bedford–Dadok and independently by Saerens–Zame in 1987. They have constructed s...

متن کامل

On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces

We present a large class of homogeneous 2-nondegenerate CR-manifolds M , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CRequivalence between domains U,V inM extends to a global real-analytic CR-automorphism ofM . We show that this class containsG-orbits in Hermitian symmetric spaces Z of compact type, where G is a real form of the complex L...

متن کامل

Cr Manifolds with Noncompact Connected Automorphism Groups

The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater than 3, it has been pointed out by D. Burns that this result follows from known results on biholomorphism groups of complex manifolds with boundary and the f...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008