Splitting theorem for Ricci soliton

Let (M, g, f) be a gradient Ricci soliton \nabla ^2 f+Ric=\lambda g with \lambda \in \{\frac {1}{2}, 0, -\frac {1}{2}\}. Suppose there is a geodesic line \gamma : (-\infty , \infty )\rightarrow M satisfying \begin{eqnarray*} \liminf _{t\rightarrow \infty }\int _0^{t}Ric(\gamma ’(s), \gamma ’(s))ds +\liminf _{t\rightarrow -\infty }\int _{t}^{0}Ric(\gamma ’(s), \gamma ’(s))ds \geq 0, \end{eqnarray*} then (M, g, f) splits off a line isometrically.