A class of generalised Killing spinors determined by the Ricci tensor and the metric

@misc{artacho2026class,
  title = {{A class of generalised Killing spinors determined by the Ricci tensor and the metric}},
  author = {Diego Artacho and Jihun Kim},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29274},
  eprint = {2609.29274},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29274},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - A class of generalised Killing spinors determined by the Ricci tensor and the metric
AU  - Diego Artacho
AU  - Jihun Kim
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29274
UR  - https://arxiv.org/abs/2609.29274
AB  - We introduce a class of generalised Killing spinors, termed affine Killing spinors (AKS), for which the associated endomorphism is a constant linear combination of the Ricci endomorphism and the identity map. We classify Riemannian spin manifolds admitting an AKS under two additional curvature hypotheses: harmonic curvature and local conformal flatness. Furthermore, we characterise Riemannian spin manifolds that admit a non-zero parallel one-form and an AKS. Additionally, we prove that in dimension three every curvature-homogeneous manifold carrying an AKS is locally homogeneous. Finally, we provide a complete classification of three-dimensional Lie groups equipped with a Bianchi metric admitting an invariant AKS.
ER  -