  Given the Euclidean space $\R^{2n+2}$ endowed with a constant symplectic
structure and the standard flat connection, and given a polynomial of degree 2
on that space, Baguis and Cahen have defined a reduction procedure which yields
a symplectic manifold endowed with a Ricci-type connection. We observe that any
symplectic manifold of dimension greater than 2 endowed with a symplectic
connection of Ricci-type is locally given by a local version of such a
reduction.
  We also consider the reverse of this reduction procedure, an induction
procedure: we construct globally on a symplectic manifold endowed with a
connection of Ricci-type $(M,\omega,\nabla)$ a circle or a line bundle which
embeds in a flat symplectic manifold $(P,\mu ,\nabla^1)$ as the zero set of a
function whose third covariant derivative vanishes, in such a way that
$(M,\omega,\nabla)$ is obtained by reduction from $(P,\mu ,\nabla^1)$.
  We further develop the particular case of symmetric symplectic manifolds with
Ricci-type connections.
