Some geometric vector fields on 5-dimensional 2-step homogeneous nilmanifolds

Ghodratallah Fasihi-Ramandi; Hajar Ghahremani-Gol; Ghodratallah Fasihi-Ramandi; Hajar Ghahremani-Gol

doi:10.3934/math.2020036

AIMS Mathematics

2020, Volume 5, Issue 1: 546-556. doi: 10.3934/math.2020036

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Research article

Some geometric vector fields on 5-dimensional 2-step homogeneous nilmanifolds

Ghodratallah Fasihi-Ramandi ^{1
,
,},
Hajar Ghahremani-Gol ²

1.
Department of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran
2.
Department of Mathematics, Shahed University, Tehran, Iran

Received: 10 August 2017 Accepted: 29 November 2019 Published: 12 December 2019
MSC : 53Bxx, 22Exx

In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5. We show that there is not any invariant concurrent vector field on such spaces. Our results show that in these manifolds each invariant conformal vector field is Killing and every invariant projective field is affine. Also, the space of some other invariant geometric fields such as affine, Killing, and harmonic vector fields on the manifolds are determined.
- nilmanifolds,
- two-step nilpotent Lie groups,
- geometric vector fields,
- concurrent vector field
Citation: Ghodratallah Fasihi-Ramandi, Hajar Ghahremani-Gol. Some geometric vector fields on 5-dimensional 2-step homogeneous nilmanifolds[J]. AIMS Mathematics, 2020, 5(1): 546-556. doi: 10.3934/math.2020036

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Abstract

In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5. We show that there is not any invariant concurrent vector field on such spaces. Our results show that in these manifolds each invariant conformal vector field is Killing and every invariant projective field is affine. Also, the space of some other invariant geometric fields such as affine, Killing, and harmonic vector fields on the manifolds are determined.

References

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