Let $(M,g)$ be a smooth Riemannian manifold, let $f: M \to \mathbb{R}$ be a smooth function, and let $\lambda \in \mathbb{R}$ be constant. Suppose $(M,g,f)$ is a gradient Ricci soliton satisfying
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\begin{align*}
\operatorname{Ric}_g+\operatorname{Hess}_g f=\lambda g.
\end{align*}
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Then the function
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\begin{align*}
R_g+|\nabla f|_g^2-2\lambda f
\end{align*}