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PreprintCC BY 4.0arXiv

Diffeomorphism Group Actions on Para-Kähler Structures: Lifts and Induced Dynamics on 3-Webs

  • Bertuel Tangue Ndawa
  • Ferdinand Ngakeu
  • Nasser Saipele Nansidi
  • Thomas Bouetou Bouetou
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Abstract

Let M be a smooth manifold equipped with a para-Kähler structure. We define an action of the diffeomorphism group Diff(M) on the space of para-Kähler structures and prove that this action preserves the associated affine structures. Although this result is well known, we provide a proof based on this action, showing in particular that an isometry commutes with the Levi--Civita connection. We then construct several natural liftings of this action to the tangent bundle TM, the cotangent bundle T*M, and the Whitney sum E=TM⊕ T*M. In certain cases, these lifted actions induce natural dynamical systems on a distinguished class of $3$-webs.

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Cite

BibTeXRIS
BibTeX
@misc{ndawa2026diffeomorphism,
  title = {{Diffeomorphism Group Actions on Para-Kähler Structures: Lifts and Induced Dynamics on 3-Webs}},
  author = {Bertuel Tangue Ndawa and Ferdinand Ngakeu and Nasser Saipele Nansidi and Thomas Bouetou Bouetou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03573},
  eprint = {2609.03573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03573},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Diffeomorphism Group Actions on Para-Kähler Structures: Lifts and Induced Dynamics on 3-Webs
AU  - Bertuel Tangue Ndawa
AU  - Ferdinand Ngakeu
AU  - Nasser Saipele Nansidi
AU  - Thomas Bouetou Bouetou
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.03573
UR  - https://arxiv.org/abs/2609.03573
AB  - Let M be a smooth manifold equipped with a para-Kähler structure. We define an action of the diffeomorphism group Diff(M) on the space of para-Kähler structures and prove that this action preserves the associated affine structures. Although this result is well known, we provide a proof based on this action, showing in particular that an isometry commutes with the Levi--Civita connection. We then construct several natural liftings of this action to the tangent bundle TM, the cotangent bundle T^*M, and the Whitney sum E=TM⊕ T^*M. In certain cases, these lifted actions induce natural dynamical systems on a distinguished class of $3$-webs.
ER  -