Cosmological data have provided new constraints on the number of neutrino species and the neutrino mass .
However these constraints depend on assumptions related to the underlying cosmology .
Since a correlation is expected between the number of effective neutrinos N _ { eff } , the neutrino mass \sum m _ { \nu } , and the curvature of the universe \Omega _ { k } , it is useful to investigate the current constraints in the framework of a non-flat universe .
In this paper we update the constraints on neutrino parameters by making use of the latest cosmic microwave background ( CMB ) data from the ACT and SPT experiments and consider the possibility of a universe with non-zero curvature .
We first place new constraints on N _ { eff } and \Omega _ { k } , with N _ { eff } = 4.03 \pm 0.45 and 10 ^ { 3 } \Omega _ { k } = -4.46 \pm 5.24 .
Thus , even when \Omega _ { k } is allowed to vary , N _ { eff } = 3 is still disfavored with 95 % confidence .
We then investigate the correlation between neutrino mass and curvature that shifts the 95 \% upper limit of \sum m _ { \nu } < 0.45 eV to \sum m _ { \nu } < 0.95 eV .
Thus , the impact of assuming flatness in neutrino cosmology is significant and an essential consideration with future experiments .