Abstract
Three-dimensional Harvey-Lawson submanifolds were introduced in an earlier paper by Akbulut and Salur [1], as examples of Lagrangian-type manifolds inside a G2 manifold. In this paper, we discuss these as well as two other similar types of submanifolds of G2 and Spin(7) manifolds and their deformations. We first show 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. We then introduce a new class of Lagrangian-type four-dimensional submanifolds of M, call them RS-submanifolds, and prove that the space of deformations of a smooth, compact, orientable RS-submanifold of a G2 manifold M can be identified with the space of closed 3-forms on RS. Finally, we describe an analogous setting for Spin(7) manifolds by defining a new class of Lagrangian-type four-dimensional submanifolds of a Spin(7) manifold N, which we call L-submanifolds. We show that the space of deformations of a smooth, compact, orientable L-submanifold of N can be identified with the space of closed 3-forms on L.