  By revisiting the notion of generalized second fundamental form originally
introduced by Hutchinson for a special class of integral varifolds, we define a
weak curvature tensor that is particularly well-suited for being extended to
general varifolds of any dimension and codimension through regularization. The
resulting approximate second fundamental forms are defined not only for
piecewise-smooth surfaces, but also for datasets of very general type (like,
e.g., point clouds). We obtain explicitly computable formulas for both weak and
approximate curvature tensors, we exhibit structural properties and prove
convergence results, and lastly we provide some numerical tests on point clouds
that confirm the generality and effectiveness of our approach.
