Generalized Killing spinors associated with the Ricci tensor

@misc{imada2026generalized,
  title = {{Generalized Killing spinors associated with the Ricci tensor}},
  author = {Natsuki Imada},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.20694},
  eprint = {2605.20694},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.20694},
}

TY  - UNPB
TI  - Generalized Killing spinors associated with the Ricci tensor
AU  - Natsuki Imada
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2605.20694
UR  - https://arxiv.org/abs/2605.20694
AB  - 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.
ER  -