  The present solar and atmospheric neutrino data together with the LSND
results and the presence of hot dark matter (HDM) suggest the existence of a
sterile neutrino at the eV scale. We have reanalysed the effect of resonant
{\sl sterile} neutrino conversions induced by neutrino magnetic moments in a
type-II supernova. We analyse the implications of $\nu_e-\nu_s$ and
$\bar{\nu}_e-\bar{\nu}_s$ ($\nu_s$ denotes sterile neutrino) conversions for
the supernova shock re-heating, the detected $\bar\nu_e$ signal from SN1987A
and the $r$-process nucleosynthesis hypothesis. Using reasonable magnetic field
profiles we determine the sensitivity of these three arguments to the relevant
neutrino parameters, i.e. the value of the transition magnetic moment and the
$\nu_e-\nu_s$ mass difference $\Delta m^2 \equiv \Delta m^2_{LSND/HDM}$
