Jacobi-type vector fields on $ \mathbb{H}^3 $ and $ \mathbb{R}^3 $

Yaning Wang; Yingdong Zhang; Yaning Wang; Yingdong Zhang

doi:10.3934/math.2021690

AIMS Mathematics

2021, Volume 6, Issue 11: 11894-11903. doi: 10.3934/math.2021690

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Research article

Jacobi-type vector fields on $ \mathbb{H}^3 $ and $ \mathbb{R}^3 $

Yaning Wang ^,,
Yingdong Zhang ^,

School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China

Received: 31 May 2021 Accepted: 03 August 2021 Published: 16 August 2021
MSC : 53C15, 53C25, 53B21

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.
- Jacobi-type vector field,
- Killing vector field,
- hyperbolic 3-space,
- Euclidean 3-space
Citation: Yaning Wang, Yingdong Zhang. Jacobi-type vector fields on $ \mathbb{H}^3 $ and $ \mathbb{R}^3 $[J]. AIMS Mathematics, 2021, 6(11): 11894-11903. doi: 10.3934/math.2021690

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Abstract

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.

References

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