Integrable G² Structures on 7-dimensional 3-Sasakian Manifolds

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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.

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G² group , G² structure , 3 , Sasakian structure

Journal Of Natural an‎d Applied Sciences

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Journal Of Natural an‎d Applied Sciences