Generalized Killing spinors associated with the Ricci tensor

TL;DR

This paper introduces Ricci Killing spinors on Riemannian spin manifolds, establishing their existence on certain Sasakian manifolds and providing new examples of manifolds with generalized Killing spinors.

Contribution

It defines Ricci Killing spinors, proves their existence on specific Sasakian manifolds, and expands the class of manifolds known to admit generalized Killing spinors.

Findings

Existence of Ricci Killing spinors on certain Sasakian manifolds

New examples of manifolds with generalized Killing spinors

Ricci Killing spinors form a class between generalized and standard Killing spinors

Abstract

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.