Research article

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

  • 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.

    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

    Related Papers:

  • 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.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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