  Models of induced-gravity inflation are formulated within Supergravity
employing as inflaton the Higgs field which leads to a spontaneous breaking of
a U(1)B-L symmetry at Mgut=2x10^16 GeV. We use a renormalizable superpotential,
fixed by a U(1) R symmetry, and Kahler potentials which exhibit a quadratic
non-minimal coupling to gravity with or without an independent kinetic mixing
in the inflaton sector. In both cases we find inflationary solutions of
Starobinsky type whereas in the latter case, others (more marginal) which
resemble those of linear inflation arise too. In all cases the inflaton mass is
predicted to be of the order of 10^13~GeV. Extending the superpotential of the
model with suitable terms, we show how the MSSM mu parameter can be generated.
Also, non-thermal leptogenesis can be successfully realized, provided that the
gravitino is heavier than about 10 TeV.
