Paracomplex Structures and Affine Symmetric Spaces-猫眼课题宝

仿复结构和仿射对称空间

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1985

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S. Kaneyuki;M. Kozai

$T^{pm}(M)$ / $p$。如果由$T^{pm}(M)$定义的$M$上的分布都是完全可积的，则这个几乎副复结构称为副复结构。这两种结构最初是由$P$引入的。Libermann于1952年（[5],[6]），用几乎复杂或复杂的结构来类比。Libermann还引入了parahertian metrics和parakahler metrics的概念，尽管有些模糊，它们是厄米度量和K"ahler度量的准复类似物。应该注意的是，副卡勒流形具有自然的辛结构。因此，主要的兴趣是人们可以在多大程度上发展副复流形理论与复流形理论并行。本文引入了一类仿射对称空间，称为拟厄米对称空间，是厄米对称空间的拟复模拟。本文讨论了准复杂结构的一些定义和基本性质。在s2中，我们给出了对称空间的定义，并包含了李代数的考虑。在s3中，我们给出了仿射对称协集空间的一个群论刻画

$T^{pm}(M)$ over $p$ . If the distributions on $M$ defined by $T^{pm}(M)$ are both completely integrable, then the almost paracomplex structure is called a paracomplex structure. These two structures were originally introduced by $P$. Libermann in 1952 ([5], [6]), in analogy with almost complex or complex structures. Libermann also introduced, although in somewhat vague fashion, the notions of parahermitian metrics and parakahler metrics, which are the paracomplex analogues of hermitian and K"ahler metrics. It should be noted that a parakahler manifold has naturally a symplectic structure. The main interest is thus to what extent one can develop the theory of paracomplex manifolds in parallel with the theory of complex manifolds. In this article, we introduce a class of affine symmetric spaces, called parahermitian symmetric spaces, a paracomplex analogue of hermitian symmetric spaces. S 1 is devoted to some definitions and basic properties on paracomplex structures. In S 2 we give the definition of parahermitian symmetric spaces and include Lie algebraic considerations. In S 3 we give a group-theoretic characterization for an affine symmetric coset space

Paracomplex Structures and Affine Symmetric Spaces

仿复结构和仿射对称空间

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