Deformations of Lagrangian Type Submanifolds inside G2 manifolds

Abstract

3-dimensional Harvey Lawson submanifolds were introduced in an earlier paper by Akbulut-Salur, as examples of Lagrangian-type manifolds inside G2 manifold. In this paper, 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 4-dimensional submanifolds inside G2, call them RS submanifolds and prove 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.