Jacobi-type vector fields on \(\mathbb{H}^3\) and \(\mathbb{R}^3\). (English) Zbl 1510.53031
Summary: In this paper, we determine the Jacobi-type vector fields on the hyperbolic 3-space \(\mathbb{H}^3\) and the Euclidean 3-space \(\mathbb{R}^3 \), respectively. In terms of this, infinitely many non-trivial Jacobi-type vector fields are given.
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53B21 | Methods of local Riemannian geometry |
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