Search for CP violation in the decay $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$

A search for CP violation in the phase space of the decay $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ is reported using $pp$ collision data, corresponding to an integrated luminosity of 1.0 fb${}^{-1}$, collected by the LHCb experiment at a centre-of-mass energy of 7 TeV. The Dalitz plot distributions for $3.1\times 10^6$ $D^{+}$ and $D^{-}$ candidates are compared with binned and unbinned model-independent techniques. No evidence for CP violation is found.