  Using the 5 year WMAP data, we re-investigate claims of non-Gaussianities and
asymmetries detected in local curvature statistics of the 1 year WMAP data. In
Hansen et al 2004, it was found that the northern ecliptic hemisphere was
non-Gaussian at the ~1% level testing the densities of hill-, lake and saddle
points based on the second derivatives of the CMB temperature map. The 5 year
WMAP data has a much lower noise level and better control of systematics. Using
these, we find that the anomalies are still present at a consistent level. Also
the direction of maximum non-Gaussianity remains. Due to limited availability
of computer resources, Hansen et al. 2004 were unable to calculate the full
covariance matrix for the chi^2 test used. Here we apply the full covariance
matrix instead of the diagonal approximation and find that the
non-Gaussianities disappear and there is no preferred non-Gaussian direction.
We compare with simulations of weak lensing to see if this may cause the
observed non-Gaussianity when using diagonal covariance matrix. We conclude
that weak lensing does not produce non-Gaussianity in the local curvature
statistics at the scales investigated in this paper. The cause of the
non-Gaussian detection in the case of a diagonal matrix remains unclear.
