Dirac Operator on a 7-Manifold with Deformed G₂ Structure

In this work, we consider the deforming of a G2 structure by a vector field on a 7-manifold. To obtain the metric corresponding to deformed G₂ structure, a new map is defined. By using this new map, the co- variant derivatives on associated spinor bundles are compared. Then, the relation between Dirac operators on spinor bundles are investigated under some restrictions.