  When considered as submanifolds of Euclidean space, the Riemannian geometry
of the round sphere and the Clifford torus may be formulated in terms of
Poisson algebraic expressions involving the embedding coordinates, and a
central object is the projection operator, projecting tangent vectors in the
ambient space onto the tangent space of the submanifold. In this note, we point
out that there exist noncommutative analogues of these projection operators,
which implies a very natural definition of noncommutative tangent spaces as
particular projective modules. These modules carry an induced connection from
Euclidean space, and we compute its scalar curvature.
