Cocalibrated \(G_2\)-manifolds with Ricci flat characteristic connection (Q2844465)

In this article, \(7\)-dimensional cocalibrated \(G_2\)-manifolds \(M\) are studied. Any such manifold admits a unique connection \(\nabla\) with skew-symmetric torsion and \(\nabla\)-parallel spinor field. The author considers the special case when the \(\nabla\)-Ricci tensor vanishes and investigates the geometry of these manifolds when there are three \(\nabla\)-parallel vector fields or two special \(\nabla\)-parallel vector fields. Classifications are given under additional assumptions.