In this paper, Gaussianity of eigenmodes and non-Gaussianity in the Cosmic
Microwave Background (CMB) temperature fluctuations in two smallest compact
hyperbolic (CH) models are investigated. First, it is numerically found that
the expansion coefficients of low-lying eigenmodes on the two CH manifolds
behave as if they are Gaussian random numbers at almost all the places. Next,
non-Gaussianity of the temperature fluctuations in the (l,m) space in these
models is studied. Assuming that the initial fluctuations are Gaussian, the
real expansion coefficients b_{l m} of the temperature fluctuations in the sky
are found to be distinctively non-Gaussian. In particular, the cosmic variances
are found to be much larger than that for Gaussian models. On the other hand,
the anisotropic structure is vastly erased if one averages the fluctuations at
a number of different observing points because of the Gaussian
pseudo-randomness of the eigenmodes. Thus the dominant contribution to the
two-point correlation functions comes from the isotropic terms described by the
angular power spectra C_l. Finally, topological quantities: the total length
and the genus of isotemperature contours are investigated. The variances of
total length and genus at high and low threshold levels are found to be
considerably larger than that of Gaussian models while the means almost agree
with them.Comment: 22 pages, 18 figures (eps files). Typos correcte
