Sums of Recursion Operators
Sums of Recursion Operators
复制标题
递归运算符的和
DOI：
10.11650/tjm/7827
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发表时间：
2017-08
影响因子：
0.4
通讯作者：
Hai-Long Her
中科院分区：
文献类型：
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作者：
Hai-Long Her
设（，，）是一个2-维光滑流形，它具有一对由递归算子∈End（）交织的辛形式和.𝑛𝐴𝜔我们考虑一个余维2子流形𝑄，𝑀它具有那些限制辛形式（𝜔|𝑄, 𝜏|𝑄).假设是-不变的。𝑇𝑄我们称元组（，）为辛递归数据。𝜏𝜔𝑀本文考虑了两个辛递归数据（，）和（，）的纤维连通和问题.𝑄𝜏𝜔𝐴𝑄𝜏𝜔𝑀有趣的是考虑潜在的应用，这一结果可积系统和数学弦理论。
Let (𝑀, 𝜔, 𝜏)𝐴be a 2𝑛-dimensional smooth manifold with a pair of symplectic forms 𝜔 and 𝜏 intertwined by a recursion operator 𝐴 ∈ End(𝑇𝑀). We consider a codimension two submanifolds 𝑄 ⊂ 𝑀 with those restricted symplectic forms (𝜔|𝑄, 𝜏|𝑄). Assume that 𝑇𝑄 is 𝐴-invariant. We call the tuple (𝑀, 𝜔, 𝜏, 𝑄)𝐴symplectic-recursion data. In this paper, we consider the problem of fibre connected sum of such two symplectic-recursion data (𝑀₀, 𝜔₀, 𝜏₀, 𝑄₀)𝐴₀and (𝑀₁, 𝜔₁, 𝜏₁,𝑄₁)𝐴₁. It is interesting to consider potential applications of this result to integrable systems and mathematical string theory.