Blow-ups and infinitesimal automorphisms of CR-manifolds

被引:6
|
作者
Kruglikov, Boris [1 ]
机构
[1] UiT Arctic Univ Norway, Dept Math & Stat, N-9037 Tromso, Norway
关键词
Real hypersurface in complex space; CR-automorphism; Holomorphic vector field; Submaximal symmetry dimension; Parabolic subalgebra; Gap phenomenon; HOLOMORPHIC MAPPINGS; POLYNOMIAL-MODELS; HYPERSURFACES; SUBMANIFOLDS;
D O I
10.1007/s00209-020-02488-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For a real-analytic connected CR-hypersurface M of CR-dimension n >= 1 having a point of Levi-nondegeneracy the following alternative is demonstrated for its symmetry algebra s = s(M): (i) either dim s = n(2) + 4n + 3 and M is spherical everywhere; (ii) or dim s <= n(2) + 2n + 2 + delta(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.
引用
收藏
页码:1701 / 1724
页数:24
相关论文
共 50 条
  • [41] HOMOGENEOUS CR-MANIFOLDS
    AZAD, H
    HUCKLEBERRY, A
    RICHTHOFER, W
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1985, 358 : 125 - 154
  • [42] Models for CR-manifolds of type (1,K) for 3≤K≤7 and their automorphisms
    E. N. Shananina
    Mathematical Notes, 2000, 67 : 382 - 388
  • [43] Extremal Graphs for Blow-Ups of Keyrings
    Ni, Zhenyu
    Kang, Liying
    Shan, Erfang
    Zhu, Hui
    GRAPHS AND COMBINATORICS, 2020, 36 (06) : 1827 - 1853
  • [44] Two inequalities for a sequence of blow-ups
    A. V. Pukhlikov
    Mathematical Notes, 2015, 97 : 970 - 973
  • [45] b-STABILITY AND BLOW-UPS
    Donaldson, S. K.
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2014, 57 (01) : 125 - 137
  • [46] Spacetime singularities and curvature blow-ups
    Racz, Istvan
    GENERAL RELATIVITY AND GRAVITATION, 2023, 55 (01)
  • [47] Tiling transitive tournaments and their blow-ups
    Yuster, R
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2003, 20 (02): : 121 - 133
  • [48] Spacetime singularities and curvature blow-ups
    István Rácz
    General Relativity and Gravitation, 2023, 55
  • [49] Extremal Graphs for Blow-Ups of Keyrings
    Zhenyu Ni
    Liying Kang
    Erfang Shan
    Hui Zhu
    Graphs and Combinatorics, 2020, 36 : 1827 - 1853
  • [50] ON THE FINITE GENERATION OF SYMBOLIC BLOW-UPS
    HUNEKE, C
    MATHEMATISCHE ZEITSCHRIFT, 1982, 179 (04) : 465 - 472