Levi--Tanaka algebras and homogeneous manifolds
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- 作者：C. Medori and M. MACINOVICH
- 关键词：C R manifold ; Levi ; Tanaka algebra.
- 刊名：Compositio Mathematica
- 出版时间：1997
- 出版年：1997
- 期刊代码：4_0010437X
- 类别：ear
- 卷：109
- 期：2
- 页码：195-250
- 数据来源：sp
摘要
In this paper we take up the problem of discussing C R manifolds of arbitrary C R codimension. We closely follow the general method of N.~Tanaka, while concentrating our attention to the case of manifolds endowed with partial complex structures. This study required a deeper understanding of the structure of the Levi--Tanaka algebras, which are the canonical prolongation of pseudocomplex fundamental graded Lie algebras. These algebras enjoy special properties, the understanding of which provided also a way to build up several different examples and points to a rich field of investigations. Here we restrained further our consideration to the homogeneous models.