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PreprintCC BY 4.0arXiv

Conformal geodesics and gauged Killing-Yano forms in dimension four

  • Wojciech Kryński
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Abstract

We study the relation between conformal geodesics and conformal Killing-Yano (CKY) 2-forms on anti-self-dual conformal manifolds of dimension 4. In the flat case, twistor quadrics determine self-dual CKY forms whose zero loci contain conformal geodesics. To extend this construction to curved manifolds, we consider self-dual 2-forms with values in a line bundle and satisfying the gauged CKY equation, coupled to connections with anti-self-dual curvature. In this way we provide a local ambient characterization of non-null conformal geodesics as zero curves of gauged CKY forms, with the curvature vanishing along these curves.

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Cite

BibTeXRIS
BibTeX
@misc{krynski2026conformal,
  title = {{Conformal geodesics and gauged Killing-Yano forms in dimension four}},
  author = {Wojciech Kryński},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41008},
  eprint = {2610.41008},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41008},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Conformal geodesics and gauged Killing-Yano forms in dimension four
AU  - Wojciech Kryński
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.41008
UR  - https://arxiv.org/abs/2610.41008
AB  - We study the relation between conformal geodesics and conformal Killing-Yano (CKY) 2-forms on anti-self-dual conformal manifolds of dimension 4. In the flat case, twistor quadrics determine self-dual CKY forms whose zero loci contain conformal geodesics. To extend this construction to curved manifolds, we consider self-dual 2-forms with values in a line bundle and satisfying the gauged CKY equation, coupled to connections with anti-self-dual curvature. In this way we provide a local ambient characterization of non-null conformal geodesics as zero curves of gauged CKY forms, with the curvature vanishing along these curves.
ER  -