  We give a necessary and sufficient condition for an n-dimensional Riemannian
manifold to be isometrically immersed in S^n x R or H^n x R in terms of its
first and second fundamental forms and of the projection of the vertical vector
field on its tangent plane. We deduce the existence of a one-parameter family
of isometric minimal deformations of a given minimal surface in S^2 x R or H^2
x R, obtained by rotating the shape operator.
