Generalized Killing spinors associated with the Ricci tensor

In this paper, we introduce the notion of Ricci Killing spinors on Riemannian spin manifolds, which form a class between generalized Killing spinors and standard Killing spinors. We prove an existence theorem for Ricci Killing spinors that are not Killing spinors on a certain class of Sasakian manifolds. This yields new examples of manifolds admitting generalized Killing spinors.