AI 中文总结
本文定义扭曲挠积流形上的Lyra几乎Ricci-Bourguignon孤子，研究其扭曲函数、Lyra标度与孤子势场的相互作用，推导孤子方程分量及相关表征，得到新刚性现象与约化结果，通过例子和不存在性结果证明该相互作用的几何意义。
AI 中文摘要
本文定义了扭曲挠积流形上的Lyra几乎Ricci-Bourguignon孤子，并研究了扭曲函数、Lyra标度与孤子势场之间的相互作用。我们推导了孤子方程的水平、垂直及混合分量，得到了迹、梯度和因子继承的表征。混合方程产生了新的刚性现象：依赖基的Lyra标度保留了普通可分性障碍，而依赖纤维的标度则允许加权补偿律，该律可容纳真正不可分的扭曲函数。我们还针对共形、Killing、同调、共现及梯度势场建立了约化结果，精确的平坦与非平坦例子，以及局部和紧不存在性结果，证明了标度-扭曲相互作用的几何意义。
英文摘要
This paper defines Lyra almost Ricci-Bourguignon solitons on twisted warped product manifolds and investigates the interaction between the twisting function, the Lyra scale, and the soliton potential field. We derive the horizontal, vertical, and mixed components of the soliton equation and obtain trace, gradient, and factor-inheritance characterizations. The mixed equation yields new rigidity phenomena: a base-dependent Lyra scale preserves the ordinary separability obstruction, whereas a fiber-dependent scale admits a weighted compensation law that allows genuinely nonseparable twisting functions. We also establish Einstein reductions for conformal, Killing, homothetic, concurrent, and gradient potential fields. Exact flat and non-flat examples, together with local and compact nonexistence results, demonstrate the geometric significance of the scale?twisting interaction.
