Rota-Baxter systems are modified by the inclusion of a curvature term. It is shown that, subject to specific properties of the curvature form, curved Rota-Baxter systems $(A,R,S,\omega)$ induce associative and (left) pre-Lie products on the algebra $A$. It is also shown that if both Rota-Baxter operators coincide with each other and the curvature is $A$-bilinear, then the (modified by $R$) Hochschild cohomology ring over $A$ is a curved differential graded algebra.
"Curved Rota-Baxter systems." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 713 - 720, december 2016. https://doi.org/10.36045/bbms/1483671622