Conformal Killing--Yano Ricci solitons: Structure, compatibility, and rigidity
Abstract
We introduce a geometric structure -- a conformal Killing--Yano Ricci soliton (CKY--RS) -- that couples conformal Ricci soliton (CRS) geometry to conformal Killing--Yano (CKY) 2--forms. The soliton field of the CRS geometry is given by the divergence of the CKY 2--form. We introduce a conserved CKY--Cotton current and derive a compatibility identity relating the Cotton tensor, the CRS obstruction tensor, and the CKY 2--form. In 4--dimensional Lorentzian signature, we show that, under non-degeneracy and closedness assumptions on the CKY form, a CKY--RS structure forces the conformal representative to be locally Kerr--NUT--(A)dS. For a closed non-degenerate CKY on a Kerr--NUT--(A)dS background, the conformal deformation is necessarily trivial. For Einstein backgrounds of arbitrary dimension and signature, the conformal factor satisfies an eigenvalue equation and an Obata--type Hessian equation. If the background is also compact or a CKY orbit is periodic, the conformal factor is an invariant of the CKY--flow and we obtain simple spectral obstructions to non-trivial CKY--RS structures. From the Hessian equation, we obtain obstruction and classification results for the non-trivial conformal sector, including product/Brinkmann geometries and a Weyl--aligned branch. Finally, we give explicit constructions for static spherically symmetric geometries and BTZ backgrounds, including a CKY--RS realization with a time-dependent conformally flat representative. These results provide a geometric framework for studying CRS with hidden symmetry structure, with potential applications to exact geometries in general relativity.
Related
- Conformal Killing $2$-Forms on Compact Symmetric Spaces
- Conformal geodesics and gauged Killing-Yano forms in dimension four
- Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature
- Rigidity and Non-existence Results of λ-Translating Solitons
- Rigidity of shrinking Ricci solitons with low-dimensional focal sets
BibTeX
@misc{habibivostakolaei2026conformal,
title = {{Conformal Killing--Yano Ricci solitons: Structure, compatibility, and rigidity}},
author = {Mohammadjavad Habibivostakolaei and Abbas M. Sherif and Yen-Kheng Lim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.23424},
eprint = {2609.23424},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23424},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Conformal Killing--Yano Ricci solitons: Structure, compatibility, and rigidity
AU - Mohammadjavad Habibivostakolaei
AU - Abbas M. Sherif
AU - Yen-Kheng Lim
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.23424
UR - https://arxiv.org/abs/2609.23424
AB - We introduce a geometric structure -- a conformal Killing--Yano Ricci soliton (CKY--RS) -- that couples conformal Ricci soliton (CRS) geometry to conformal Killing--Yano (CKY) 2--forms. The soliton field of the CRS geometry is given by the divergence of the CKY 2--form. We introduce a conserved CKY--Cotton current and derive a compatibility identity relating the Cotton tensor, the CRS obstruction tensor, and the CKY 2--form. In 4--dimensional Lorentzian signature, we show that, under non-degeneracy and closedness assumptions on the CKY form, a CKY--RS structure forces the conformal representative to be locally Kerr--NUT--(A)dS. For a closed non-degenerate CKY on a Kerr--NUT--(A)dS background, the conformal deformation is necessarily trivial. For Einstein backgrounds of arbitrary dimension and signature, the conformal factor satisfies an eigenvalue equation and an Obata--type Hessian equation. If the background is also compact or a CKY orbit is periodic, the conformal factor is an invariant of the CKY--flow and we obtain simple spectral obstructions to non-trivial CKY--RS structures. From the Hessian equation, we obtain obstruction and classification results for the non-trivial conformal sector, including product/Brinkmann geometries and a Weyl--aligned branch. Finally, we give explicit constructions for static spherically symmetric geometries and BTZ backgrounds, including a CKY--RS realization with a time-dependent conformally flat representative. These results provide a geometric framework for studying CRS with hidden symmetry structure, with potential applications to exact geometries in general relativity.
ER -