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<p>In the literature, there are several versions of the concept of Jacobi fields (or Jacobi sections) for semisprays on Lie algebroids, each with particular approaches and applications. In this paper, an alternative definition of Jacobi fields for semisprays on Lie algebroids is presented, providing a more natural generalization of the classical definition of Jacobi fields for geodesic curves. This new perspective not only broadens the theoretical framework but also allows the generalization of some results in Riemannian geometry. Finally, the relationship between our definition and other versions reported in the literature is explored, highlighting its applications.</p>

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Jacobi fields, sprays and connections on Lie algebroids

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Misael Avendaño-Camacho,
  • Jhonny Kama-Mamani

摘要

In the literature, there are several versions of the concept of Jacobi fields (or Jacobi sections) for semisprays on Lie algebroids, each with particular approaches and applications. In this paper, an alternative definition of Jacobi fields for semisprays on Lie algebroids is presented, providing a more natural generalization of the classical definition of Jacobi fields for geodesic curves. This new perspective not only broadens the theoretical framework but also allows the generalization of some results in Riemannian geometry. Finally, the relationship between our definition and other versions reported in the literature is explored, highlighting its applications.