Recent in situ spacecraft observations and the analysis of the galactic cosmic ray intensity at Earth have shown that the heliospheric magnetic field exhibited a north-south asymmetry and that the heliospheric current sheet was inclined with respect to the solar equator during the years around the last sunspot minimum (1995--1996). In this paper we show that both heliospheric characteristics are due to the particular way the solar magnetic field evolves. The north-south asymmetry can be explained with the evolution of the quadrupolar component of the field in the solar magnetosphere and the inclination of the heliospheric current sheet could be a result of the presence of an inclined relic dipolar field in the Sun, as has been suggested by Bravo and Stewart [1995>. ¿ 2000 American Geophysical Union