On Seven Dimensional 3-Sasakian Manifolds
Özet
3-Sasakian manifolds in dimension seven have cocalibrated and nearly parallel G(2)-structures. In this work, cocalibrated G(2)-structure is deformed by one of the characteristic vector fields of the 3-Sasakian structure and a new G(2) structure is obtained whose metric has negative scalar curvature. In addition, the new G(2) structure has a nonzero Killing vector field. Then, by using this deformation, new covariant derivative on the spinor bundle is obtained and the new Dirac operator is written in terms of the Dirac operator before deformation.
