发表机构
KU Leuven（荷语鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入仿射Killing旋量（AKS），在调和曲率和局部共形平坦条件下分类允许AKS的黎曼自旋流形，刻画带平行1-形式的流形，并证明三维曲率齐次流形的局部齐次性及Bianchi度量的完整分类。
AI 中文摘要
我们引入一类广义Killing旋量，称为仿射Killing旋量（AKS），其相关的自同态是Ricci自同态与恒等映射的常系数线性组合。我们在两个附加曲率假设下对允许AKS的黎曼自旋流形进行分类：调和曲率和局部共形平坦。此外，我们刻画了允许非零平行1-形式和AKS的黎曼自旋流形。进一步，我们证明了在三维中，每个携带AKS的曲率齐次流形都是局部齐次的。最后，我们提供了配备Bianchi度量的三维李群允许不变AKS的完整分类。
英文摘要
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.
Comments12 pages
