Article (Scientific journals)
A characterization of CR quadrics with a symmetry property
Altomani, Andrea; Medori, Constantino
2012In Journal of Geometric Analysis, 22 (3), p. 892-909
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Keywords :
CR quadric; Homogeneous CR manifold; Levi; Tanaka algebra; Involutive automorphism
Abstract :
[en] We study CR quadrics satisfying a symmetry property (S~) which is slightly weaker than the symmetry property (S), recently introduced by W. Kaup, which requires the existence of an automorphism reversing the gradation of the Lie algebra of infinitesimal automorphisms of the quadric. We characterize quadrics satisfying the (S~) property in terms of their Levi–Tanaka algebras. In many cases the (S~) property implies the (S) property; this holds in particular for compact quadrics. We also give a new example of a quadric such that the dimension of the algebra of positive-degree infinitesimal automorphisms is larger than the dimension of the quadric.
Disciplines :
Mathematics
Author, co-author :
Altomani, Andrea ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Medori, Constantino
External co-authors :
yes
Language :
English
Title :
A characterization of CR quadrics with a symmetry property
Publication date :
July 2012
Journal title :
Journal of Geometric Analysis
ISSN :
1559-002X
Publisher :
Springer New York LLC, New York, United States - New York
Volume :
22
Issue :
3
Pages :
892-909
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 25 March 2016

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