论文标题
$ \ mathbb {c}^3 $中简单传递的Levi非排效机突出的分类
Classification of simply-transitive Levi non-degenerate hypersurfaces in $\mathbb{C}^3$
论文作者
论文摘要
Holomororphor均匀的Cr真实横向表面$ M^3 \ subset \ Mathbb {C}^2 $在1932年被列利·卡坦（ÉlieCartan抽象谎言代数的分类。我们方法的核心是基本（复杂）四分之一张量的新的无坐标公式。我们的最终结果具有独特的（Levi definite）非管模型，为此我们证明了与平面等级几何形状的几何关系。
Holomorphically homogeneous CR real hypersurfaces $M^3 \subset \mathbb{C}^2$ were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi non-degenerate hypersurfaces $M^5 \subset \mathbb{C}^3$ using a novel Lie algebraic approach independent of any earlier classifications of abstract Lie algebras. Central to our approach is a new coordinate-free formula for the fundamental (complexified) quartic tensor. Our final result has a unique (Levi-indefinite) non-tubular model, for which we demonstrate geometric relations to planar equi-affine geometry.
