A spectral aqua-planet atmospheric general circulation model (AGCM) is forced with a series of zonally constant sea surface temperature (SST) distributions which are symmetric about the equator. For every oceanic forcing, the AGCM is run twice; a first time keeping all spectral modes and a second time with only the zonally symmetric ones. Parameterizations and boundary conditions remain the same in all cases thus allowing a consistent comparison of 3-D and 2-D flows. The comparative study shows that the structure of the tropical mean state of the full model is basically captured by the zonally symmetric model and that eddy fields merely modify this structure. This shows that the structure of the tropical mean state is mainly determined by the shape of the effective SST forcing. We confirm previous studies where the shape and strength of the Hadley circulation is comparable in the 3-D and 2-D experiments for cases with a well pronounced single ITCZ. So the underestimation of the Hadley circulation often found in idealized zonally symmetric models is not only due to the neglect of large-scale eddy fields. A new result is that both the full as well as the zonally symmetric model show the phenomenon of ITCZ splitting if the SST distribution gets flat enough at the equator. So ITCZ splitting can be explained by purely zonally symmetric mechanisms and is not necessarily induced by eddy fields. Eddies seem to stabilize single ITCZ circulation regimes. For SST distributions where ITCZ splitting occurs, multiple states exist in the zonally symmetric model. The atmosphere switches, for the same SST, between a single and double ITCZ state introducing a long-term variability in the tropics without the influence of mid-latitudes and without atmosphere-ocean coupling.