Neutrinos from SN1987A, Earth matter effects and the LMA solution of the solar neutrino problem

We study properties of the oscillation effects in the matter of the Earth on antineutrino fluxes from supernovae. We show that these effects can provide explanation of the difference in the energy spectra of the events detected by Kamiokande-2 and IMB detectors from SN1987A as well as the absence of high-energy events with $E\gta 40$ MeV. This explanation requires the neutrino oscillation parameters $\Delta m^2$ and $\sin^2 2\theta $ to be in the region of the LMA solution of the solar neutrino problem and the normal mass hierarchy if $|U_{e 3}|^2\gta 10^{-3}$. The hierarchy can be inverted if $|U_{e 3}|^2\ll 10^{-3}$. The solution of the solar neutrino problem based on $\nu_e$-conversion to a pure sterile state is disfavoured by SN1987A data.