The Geometry of Recursion Operators
The Geometry of Recursion Operators
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DOI：
10.1007/s00220-008-0477-6
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发表时间：
2007-03
影响因子：
2.4
通讯作者：
G. Bande;D. Kotschick
中科院分区：
文献类型：
--
作者：
G. Bande;D. Kotschick
我们研究交织成对的辛结构的自同态场。利用这些自同态，我们证明了两族辛型的同时同构的Moser定理的一个类似。我们还考虑了由交织自同态的平方加或减单位元的辛形式对和三元组所定义的几何结构。对于形式对，我们恢复了辛对和全纯辛结构的概念。对于三元组，我们恢复了超辛结构的概念，我们还发现了三个以前没有考虑过的新结构。其中之一是超Kähler几何的辛公式，它被证明是微分或Kähler几何中通常定义的严格推广。
We study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser’s theorem for simultaneous isotopies of two families of symplectic forms. We also consider the geometric structures defined by pairs and triples of symplectic forms for which the squares of the intertwining endomorphisms are plus or minus the identity. For pairs of forms we recover the notions of symplectic pairs and of holomorphic symplectic structures. For triples we recover the notion of a hypersymplectic structure, and we also find three new structures that have not been considered before. One of these is the symplectic formulation of hyper-Kähler geometry, which turns out to be a strict generalization of the usual definition in terms of differential or Kähler geometry.