  A Cartan decomposition for symmetric pairs plays an important role to study
not only orbit geometry of the symmetric spaces but also harmonic analysis on
them. For non-symmetric reductive pairs, there are examples of generalizations
of Cartan decompositions for some spherical complex homogeneous spaces such as
complex line bundles over the complexified Hermitian symmetric spaces and
triple spaces. This paper provides new examples of a Cartan decomposition for
non-symmetric reductive pairs, namely, reductive non-symmetric spherical pairs
of rank-one type. We also show that the action of some compact group on a
non-symmetric reductive spherical homogeneous space of rank-one type is
strongly visible.
