Maximally homogeneous para-CR manifolds
Maximally homogeneous para-CR manifolds
复制标题
最大同质对 CR 流形
DOI：
10.1007/s10455-005-9009-1
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发表时间：
2006
影响因子：
0.7
通讯作者：
A. Tomassini
中科院分区：
文献类型：
--
作者：
D. Alekseevsky;C. Medori;A. Tomassini
我们将流形M上的(弱)几乎仿CR结构的概念定义为分布HM⊂TM以及HM的对合自同态的域K∈Γ(END(HM))。如果K满足可积条件，则(HM，K)称为(弱)仿CR结构。在一定的正则性条件下，几乎准CR结构可以与Tanaka结构相一致。定义了半单型的极大齐次几乎仿CR结构的概念。利用实半单李代数的适当阶次，给出了这种极大齐次几乎仿CR结构的一个分类。给出了深度为2的最大齐次结构(对应于深度为2的梯度)，并验证了可积性条件。
We define the notion of a (weak) almost para-CR structure on a manifoldMas a distributionHM⊂TMtogether with a field K ∈ Γ(End(HM)) of involutive endomorphisms ofHM. IfKsatisfies integrability conditions, then (HM,K) is called a (weak) para-CR structure. Under some regularity conditions, an almost para-CR structure can be identified with a Tanaka structure. The notion of maximally homogeneous almost para-CR structure of a semisimple type is defined. A classification of such maximally homogeneous almost para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras. All such maximally homogeneous structures of depth two (which correspond to depth two gradations) are listed and the integrability conditions are verified.