发表机构
Alexandru Ioan Cuza University; Gheorghe Asachi Technical University（亚历山德鲁·约安·库扎大学; 格奥尔基·阿萨奇理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Finsler几何中利用Frölicher-Nijenhuis形式体系，建立了Killing向量场的十二种等价刻画，并给出局部方程形式，揭示其多方面的几何本质。
AI 中文摘要
众所周知，无穷小等距变换保持黎曼或Finsler流形的许多典型几何结构。在本文中，我们确定了Finsler流形中那些被无穷小等距变换（即Killing向量场）所保持的几何结构，并且这些结构的保持性恰好刻画了此类向量场。利用Frölicher-Nijenhuis形式体系作为统一的几何框架，我们在Finsler背景下建立了Killing性质的十二种等价刻画，利用了Finsler范数、球丛、接触与辛结构、Reeb与Hamilton向量场、首次积分、齐次化近复结构以及Sasaki度量。此外，我们推导了这些刻画的局部表达式，得到了Killing方程的若干等价形式，包括标量形式、一形式形式和张量形式。在我们的方法中，这些形式中没有哪一种被视为基本的；每一种都反映了Killing条件的不同几何方面。
英文摘要
It is well known that infinitesimal isometries preserve many of the canonical geometric structures of a Riemannian or Finslerian manifold. In this paper, we identify those geometric structures of a Finslerian manifold that are preserved by an infinitesimal isometry (a Killing vector field) and whose preservation characterises such fields. Using the Frölicher-Nijenhuis formalism as a unified geometric framework, we establish twelve equivalent characterisations of the Killing property in the Finslerian setting, utilizing the Finsler norm, the sphere bundle, contact and symplectic structures, Reeb and Hamiltonian vector fields, first integrals, the homogenized almost complex structure, and the Sasaki metrics. Furthermore, we derive the local expressions of these characterisations, yielding several equivalent forms of the Killing equations, including scalar, one-form and tensorial formulations. In our approach, none of these formulations is regarded as primary; each reflects a different geometric aspect of the Killing condition.
