3-Sasakian manifolds in dimension seven, their spinors and G2-structures

It is well known that 7-dimensional 3-Sasakian manifolds carry a one-parametric family of compatible G2-structures and that they do not admit a characteristic connection. In this note, we show that there is nevertheless a distinguished cocalibrated G2-structure in this family whose characteristic connection ∇c∇c along with its parallel spinor field Ψ0Ψ0 can be used for a thorough investigation of the geometric properties of 7-dimensional 3-Sasakian manifolds. Many known and some new properties can be easily derived from the properties of ∇c∇c and of Ψ0Ψ0, yielding thus an appropriate substitute for the missing characteristic connection.