Year: 2026
Type: preprint
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 establish a rigidity result for Ricci Killing spinors and characterize simply connected Sasakian $η$-Einstein spin manifolds admitting Ricci Killing spinors. We also give a complete classification of Ricci Killing spinors on simply connected $3$-dimensional unimodular Lie groups with left-invariant Riemannian metrics. In particular, we obtain new examples of generalized Killing spinors which are not Killing spinors. Finally, for the non-Killing Ricci Killing spinors obtained in the Lie group case, we explicitly determine the corresponding Ricci-flat ambient manifolds carrying parallel spinors.
Source: arXiv (Cornell University)
Author: Imada, Natsuki
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162013148