  In an earlier paper we showed that the space of deformations of a smooth,
compact, orientable Harvey-Lawson submanifold HL in a G2 manifold M can be
identified with the direct sum of the space of smooth functions and closed
2-forms on HL. In that paper, we also introduced a new class of Lagrangian-type
4-dimensional submanifolds inside G2 manifolds, called them RS submanifolds,
and proved that the space of deformations of a smooth, compact, orientable RS
submanifold in a G2 manifold M can be identified with closed 3-forms on RS. In
this short note, we define a new class of Lagrangian-type 4-dimensional
submanifolds inside Spin(7) manifolds, which we call L-submanifolds. We show
that the space of deformations of a smooth, compact, orientable L-submanifold
in a Spin(7) manifold N can be identified with the space of closed 3-forms on
L.
