论文标题
整合Nijenhuis结构
Integrating Nijenhuis Structures
论文作者
论文摘要
nijenhuis歧管$ m $上的nijenhuis运营商是$（1,1）$ tensor $ \ Mathcal n $，其Nijenhuis-torsion消失了。 $ m $上的nijenhuis操作员$ \ Mathcal n $确定lie代数结构$（tm）_ {\ Mathcal n} $上的切线捆绑$ tm $。从这个意义上讲，nijenhuis操作员可以看作是无限的对象。在本文中，我们确定其“全球对手”。也就是说，我们表明，当Lie代数$（TM）_ {\ Mathcal n} $是可以集成的时，它将集成到配备适当的额外结构的lie groupoid，负责$ \ Mathcal n $，而Viceversa和Viceversa，viceversa，lie for lie dembroid for lie groupsoid for lie for a type $ nij $ nij nij nij nij nij（tm）操作员$ \ Mathcal n $。我们说明了整合的结果。
A Nijenhuis operator on a manifold $M$ is a $(1,1)$ tensor $\mathcal N$ whose Nijenhuis-torsion vanishes. A Nijenhuis operator $\mathcal N$ on $M$ determines a Lie algebroid structure $(TM)_{\mathcal N}$ on the tangent bundle $TM$. In this sense a Nijenhuis operator can be seen as an infinitesimal object. In this paper, we identify its "global counterpart". Namely, we show that when the Lie algebroid $(TM)_{\mathcal N}$ is integrable, then it integrates to a Lie groupoid equipped with appropriate additional structure responsible for $\mathcal N$, and viceversa, the Lie algebroid of a Lie groupoid equipped with such additional structure is of the type $(TM)_{\mathcal N}$ for some Nijenhuis operator $\mathcal N$. We illustrate our integration result in various examples.
