论文标题
Nijnehuis几何III：GL-GL-Nijenhuis操作员
Nijnehuis Geometry III: gl-regular Nijenhuis operators
论文作者
论文摘要
我们研究了nijenhuis运算符，即（1,1） - 在其他假设中，它们消失了nijenhuis扭转，即它们是gl-grog-grog-gl-groul-new-egen-valuue，即每个特征值都具有几何多重性。我们证明了坐标系的存在，其中操作员采用了第一或第二个伴随表格，并给出了对此类操作员的本地描述。我们将此本地描述应用于研究单数点。特别是，我们以二维形式获得了它们的正常形式，并发现了对闭合表面上GL规则的Nijenhuis操作员存在的拓扑限制。本文是ARXIV建议的研究计划的重要一步：1903.04603和Arxiv：1903.06411。
We study Nijenhuis operators, that is, (1,1)-tensors with vanishing Nijenhuis torsion under the additional assumption that they are gl-regular, i.e., every eigenvalue has geometric multiplicity one. We prove the existence of a coordinate system in which the operator takes first or second companion form, and give a local describtion of such operators. We apply this local description to study singular points. In particular, we obtain their normal forms in dimension two and discover topological restrictions for the existence of gl-regular Nijenhuis operators on closed surfaces. This paper is an important step in the research programme suggested in arXiv:1903.04603 and arXiv:1903.06411.
