Ellipticity of Structures in CMB Sky Maps

We study the ellipticity of contour lines in the sky maps of the cosmic microwave background (CMB) as well as other measures of elongation. The sensitivity of the elongation on the resolution of the CMB maps which depends on the pixelization and the beam profile of the detector, is investigated. It is shown that the current experimental accuracy does not allow to discriminate between cosmological models which differ in curvature by Delta Omega_tot=0.05. Analytical expressions are given for the case that the statistical properties of the CMB are those of two-dimensional Gaussian random fields.