On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections
On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections
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在非简并实超曲面上，分级李代数和嘉当连接
DOI：
10.4099/math1924.2.131
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
N. Tanaka
中科院分区：
文献类型：
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作者：
N. Tanaka
文中我们省略了定理1的证明，因为它本质上是由田中[11]实现的，并且该定理现在是熟悉的。)设Mi(i=1，2)是复流形M·L的实超曲面(在本文中，一切都将在实解析范畴中考虑)。然后我们称M1到M2的微分同胚Cp是M1到M2的同构，如果它可以扩张为M1的邻域U1到M2的邻域U2的双全纯映射ƒ？·L。此外，我们称复流形M·L的实超曲面M是非退化的，如果实超曲面M的每个点x上的李氏范数L是非退化的。这里我们回顾一下，复流形M·L的每个实超曲面M都有一个几何结构，即我们所称的伪复(或简称PC)结构。因此，非退化实超曲面的几何可以用“非退化”PC结构的几何来表示。在本文中，我们主要讨论了非退化PC结构的几何以及相关的几何，即
paper we have omitted the proof of Theorem 1 there, because it is essentially achieved by Tanaka [11] and the theorem is now familiar.) Let Mi (i=1, 2) be a real hypersurf ace of a complex manifold M•L. (In this introduction everything will be considered in the real analytic category.) Then we say that a diffeomorphism cp of M1 onto M2 is an isomorphism of M1 onto M2 if it can be extended to a biholomorphic map ƒÕ•L of a neighbor hood U1 of M1 onto a neighborhood U2 of M2. Moreover we say that a real hypersurf ace M of a complex manifold M•L is non-degenerate if the Levi f orm L at each point x of the real hypersurf ace is non-degenerate. Here we recall the fact that every real hypersurf ace M of a complex manifold M•L is endowed with a geometric structure, i.e., what we call the pseudo complex (or briefly PC) structure. Thus the geometry of non-degenerate real hypersurf aces may be represented by the geometry of "non-degenerate" PC structures. In the present paper we are mainly concerned with the geometry of non-degenerate PC structures as well as the related geometry, i.e., the