It is known since long <Rosenberg and Coleman, 1969> that one of the two sectors of the interplanetary magnetic field (IMF) observed at the Earth's orbit dominates at high heliographic latitudes during solar minimum times, reflecting the poloidal structure of the global solar magnetic field at these times. Here we find that while this latitudinal variation of the dominant IMF sector around the solar equator is valid for both solar hemispheres during the last four solar minima covered by direct observations, it is systematically more strongly developed in the northern heliographic hemisphere. This implies that the average heliospheric current sheet is shifted or coned southward during solar minimum times, suggesting that the temporary southward shift of the heliosheet found earlier by Ulysses observations in 1995 is a persistent pattern. This also implies that the open solar magnetic field is north-south asymmetric at these times, suggesting that the solar dynamo has an asymmetric component. Accordingly, the Sun with the heliosheet is like a bashful ballerina who is repeatedly trying to push her excessively high flaring skirt downward. However, the effective shift at 1 AU is only a few degrees, allowing the Rosenberg-Coleman rule to be valid, on an average, in both hemispheres during solar minima.