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PreprintarXiv licencearXiv

From quadratic integrals to Nijenhuis operators: two-dimensional dictionary

  • Dinmukhammed Akpan
Open at sourcePDFDOICite

Abstract

We construct an explicit dictionary between two local classifications in dimension two: normal forms of pseudo-Riemannian metrics with a quadratic integral of the geodesic flow and normal forms of gl-regular Nijenhuis operators. The correspondence is obtained by an explicit change of coordinates constructed from the trace and determinant of the operator.

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Cite

BibTeXRIS
BibTeX
@misc{akpan2026from,
  title = {{From quadratic integrals to Nijenhuis operators: two-dimensional dictionary}},
  author = {Dinmukhammed Akpan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05103},
  eprint = {2609.05103},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05103},
}
RIS
TY  - UNPB
TI  - From quadratic integrals to Nijenhuis operators: two-dimensional dictionary
AU  - Dinmukhammed Akpan
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05103
UR  - https://arxiv.org/abs/2609.05103
AB  - We construct an explicit dictionary between two local classifications in dimension two: normal forms of pseudo-Riemannian metrics with a quadratic integral of the geodesic flow and normal forms of gl-regular Nijenhuis operators. The correspondence is obtained by an explicit change of coordinates constructed from the trace and determinant of the operator.
ER  -