  We investigate the notion of subsystem in the framework of spectral triple as
a generalized notion of noncommutative submanifold. In the case of manifolds,
we consider several conditions on Dirac operators which turn embedded
submanifolds into isometric submanifolds. We then suggest a definition of
spectral subtriple based on the notion of submanifold algebra and the already
existing notions of Riemannian, isometric, and totally geodesic morphisms. We
have shown that our definitions work at least in some relevant almost
commutative examples.
