The study of symmetries is a well known research topic in differential geometry with relevant physical interpretations. Given a Riemannian manifold $(M,g)$, we consider pseudo‐Riemannian g‐natural metrics G on its tangent bundle $TM$ and characterize conformal, homothetic and Killing vector fields of $(TM,G)$ obtained from natural lifts of vector fields of M.

中文翻译：

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切线束上的g自然对称

对称性的研究是微分几何中具有相关物理解释的众所周知的研究主题。给定黎曼流形$（\mathrm{中号}，G）$，我们在其切线束上考虑伪黎曼g自然度量G$Ť\mathrm{中号}$ 并表征保形的，同构的和杀死的矢量场 $（Ť\mathrm{中号}，G）$从M的向量场的自然提升中获得。