  Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with
reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by
the spin representation Ad:H->\GL_R(S) of the stabilizer H. This article
studies the superizations of M_0, i.e. its extensions to a homogeneous
supermanifold M=G/H whose sheaf of superfunctions is isomorphic to
Lambda(S^*(M_0)). Here G is the Lie supergroup associated with a certain
extension of the Lie algebra of symmetry g_0 to an algebra of supersymmetry
g=g_0+g_1=g_0+S via the Kostant-Koszul construction. Each algebra of
supersymmetry naturally determines a flat connection nabla^{S} in the spin
bundle S(M_0). Killing vectors together with generalized Killing spinors (i.e.
nabla^{S}-parallel spinors) are interpreted as the values of appropriate
geometric symmetries of M, namely even and odd Killing fields. An explicit
formula for the Killing representation of the algebra of supersymmetry is
obtained, generalizing some results of Koszul. The generalized spin connection
nabla^{S} defines a superconnection on M, via the super-version of a theorem of
Wang.
