发表机构
Institute of Mathematics, Henan Academy of Sciences; School of Mathematics and Physics, Xiamen University Malaysia（河南省科学院数学研究所; 马来西亚厦门大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入共形Killing--Yano Ricci孤立子结构，建立相容性恒等式，证明在4维Lorentzian下其强制局部Kerr--NUT--(A)dS几何，并给出谱阻碍与显式构造，为研究隐藏对称性的共形Ricci孤立子提供几何框架。
AI 中文摘要
我们引入一种几何结构——共形Killing--Yano Ricci孤立子（CKY--RS）——它将共形Ricci孤立子（CRS）几何与共形Killing--Yano（CKY）2-形式耦合。CRS几何的孤立子场由CKY 2-形式的散度给出。我们引入一个守恒的CKY--Cotton流，并推导出一个相容性恒等式，该恒等式将Cotton张量、CRS阻碍张量和CKY 2-形式联系起来。在4维Lorentzian符号下，我们证明，在CKY形式的非退化性和闭性假设下，CKY--RS结构迫使共形代表局部为Kerr--NUT--(A)dS。对于Kerr--NUT--(A)dS背景上的闭非退化CKY，共形形变必然是平凡的。对于任意维数和符号的Einstein背景，共形因子满足一个特征值方程和一个Obata型Hessian方程。如果背景也是紧致的或CKY轨道是周期的，则共形因子是CKY--流的不变量，我们获得非平凡CKY--RS结构的简单谱阻碍。从Hessian方程，我们获得非平凡共形扇区的阻碍和分类结果，包括乘积/Brinkmann几何和Weyl--对齐分支。最后，我们给出静态球对称几何和BTZ背景的显式构造，包括具有时间依赖共形平坦代表的CKY--RS实现。这些结果为研究具有隐藏对称结构的CRS提供了一个几何框架，并可能应用于广义相对论中的精确几何。
英文摘要
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.
Comments24 pages
