  In this work, ruled surfaces in 3-dimensional Riemannian manifolds are
studied. We determine the expression for the extrinsic and sectional curvature
of a parametrized ruled surface, where the former one is shown to be
non-positive. We also quantify the set of ruling vector fields along a given
base curve which allows to define a relevant reference frame that we refer to
as Sannia frame. The fundamental theorem of existence and equivalence of
Sannia-ruled surfaces in terms of a system of invariants is given. The second
part of the article tackles the concept of the striction curve, which is proven
to be the set of points where the so-called Jacobi evolution function vanishes
on a ruled surface. This characterization of striction curves provides
independent proof for their existence and uniqueness in space forms and
disproves their existence or uniqueness in some other cases.
