Integrable G² Structures on 7-dimensional 3-Sasakian Manifolds

It is known that there exist canonical and nearly parallel g² structures on7-dimensional 3-sasakian manifolds. in this paper, we investigate the existence of g²structures which are neither canonical nor nearly parallel. we obtain eight new g²structures on 7-dimensional 3-sasakian manifolds which are of general type according tothe classification of g² structures by fernandez and gray. then by deforming the metricdetermined by the g² structure, we give integrable g² structures. on a manifold withintegrable g² structure, there exists a uniquely determined metric covariant derivativewith anti-symetric torsion. we write torsion tensors corresponding to metric covariantderivatives with skew-symmetric torsion. in addition, we investigate some properties oftorsion tensors.