scholarly journals Hölder estimates on CR manifolds with a diagonalizable Levi form

1990 ◽  
Vol 84 (1) ◽  
pp. 1-90 ◽  
Author(s):  
C.L Fefferman ◽  
J.J Kohn ◽  
M Machedon
Keyword(s):  
Levi Form ◽  
Cr Manifolds ◽  
Hölder Estimates

scholarly journals ON HOMOGENEOUS CR MANIFOLDS AND THEIR CR ALGEBRAS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1199-1214
Author(s):  
ANDREA ALTOMANI ◽  
COSTANTINO MEDORI
Keyword(s):  
Lie Group ◽  
Levi Form ◽  
Flag Manifold ◽  
Semisimple Lie Group ◽  
Real Form ◽  
Cr Manifolds ◽  
Geometrical Properties ◽  
Homogeneous Cr Manifolds

In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond to geometrical properties for the corresponding manifolds. We also give distinguished equivariant CR fibrations for homogeneous CR manifolds. In the second part of the paper we apply these results to minimal orbits for the action of a real form of a semisimple Lie group Ĝ on a flag manifold Ĝ/Q.

scholarly journals Blow-ups and infinitesimal automorphisms of CR-manifolds

2020 ◽  
Vol 296 (3-4) ◽  
pp. 1701-1724
Author(s):  
Boris Kruglikov
Keyword(s):  
Lie Group ◽  
Blow Up ◽  
Symmetry Algebra ◽  
Levi Form ◽  
Cr Manifolds ◽  
Parabolic Subalgebras ◽  
Degeneracy Locus ◽  
Real Analytic ◽  
Infinitesimal Automorphisms

Abstract For a real-analytic connected CR-hypersurface M of CR-dimension $$n\geqslant 1$$ n ⩾ 1 having a point of Levi-nondegeneracy the following alternative is demonstrated for its symmetry algebra $$\mathfrak {s}={\mathfrak {s}}(M)$$ s = s ( M ) : (i) either $$\dim {\mathfrak {s}}=n^2+4n+3$$ dim s = n 2 + 4 n + 3 and M is spherical everywhere; (ii) or $$\dim {\mathfrak {s}}\leqslant n^2+2n+2+\delta _{2,n}$$ dim s ⩽ n 2 + 2 n + 2 + δ 2 , n and in the case of equality M is spherical and has fixed signature of the Levi form in the complement to its Levi-degeneracy locus. A version of this result is proved for the Lie group of global automorphisms of M. Explicit examples of CR-hypersurfaces and their infinitesimal and global automorphisms realizing the bound in (ii) are constructed. We provide many other models with large symmetry using the technique of blow-up, in particular we realize all maximal parabolic subalgebras of the pseudo-unitary algebras as a symmetry.

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