  We present evolutionary models of helium accreting carbon-oxygen white dwarfs
in which we include the effects of the spin-up of the accreting star induced by
angular momentum accretion, rotationally induced chemical mixing and rotational
energy dissipation. Initial masses of 0.6 Msun and 0.8 Msun and constant
accretion rates of a few times 10^{-8} Msun/yr of helium rich matter have been
considered, which is typical for the sub-Chandrasekhar mass progenitor scenario
for Type Ia supernovae. It is found that the helium envelope in an accreting
white dwarf is heated efficiently by friction in the differentially rotating
spun-up layers. As a result, helium ignites much earlier and under much less
degenerate conditions compared to the corresponding non-rotating case.
Consequently, a helium detonation may be avoided, which questions the
sub-Chandrasekhar mass progenitor scenario for Type Ia supernovae. We discuss
implications of our results for the evolution of helium star plus white dwarf
binary systems as possible progenitors of recurrent helium novae.
