3-Sasakian manifolds in dimension seven, their spinors and G(2)-structures

摘要

It is well known that 7-dimensional 3-Sasakian manifolds carry a one-parametric family of compatible G(2)-structures and that they do not admit a characteristic connection. In this note, we show that there is nevertheless a distinguished cocalibrated G(2)-structure in this family whose characteristic connection del(c) along with its parallel spinor field Psi(0) 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 del(c) and of Psi(0), yielding thus an appropriate substitute for the missing characteristic connection.