Singularities of two-dimensional Nijenhuis operators
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913742011236352 |
|---|---|
| author | Akpan, Dinmukhammed |
| author_facet | Akpan, Dinmukhammed |
| contents | A Nijenhuis operator $L$ is a $(1,1)$-tensor field on a smooth manifold $M$ with vanishing Nijenhuis torsion ${ {\mathcal N_L}}$. At each point $x\in M$, the algebraic type of $L(x)$ is characterized by its Jordan normal form. In this paper, we study singularities of a two-dimensional Nijenhuis operator in the case when its trace has a non-zero differential at the singular point. A description of such singularities reduces to studying the smoothness of some function, which is a fraction depending on partial derivatives of the determinant of $L$. We completely describe singularities for some special classes of functions. We also obtained interesting examples of Nijenhuis operators and their singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularities of two-dimensional Nijenhuis operators Akpan, Dinmukhammed Differential Geometry A Nijenhuis operator $L$ is a $(1,1)$-tensor field on a smooth manifold $M$ with vanishing Nijenhuis torsion ${ {\mathcal N_L}}$. At each point $x\in M$, the algebraic type of $L(x)$ is characterized by its Jordan normal form. In this paper, we study singularities of a two-dimensional Nijenhuis operator in the case when its trace has a non-zero differential at the singular point. A description of such singularities reduces to studying the smoothness of some function, which is a fraction depending on partial derivatives of the determinant of $L$. We completely describe singularities for some special classes of functions. We also obtained interesting examples of Nijenhuis operators and their singularities. |
| title | Singularities of two-dimensional Nijenhuis operators |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.11852 |