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Slant Null Curves on Normal Almost Contact B-Metric 3-Manifolds with Parallel Reeb Vector Field

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Abstract

In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector field. We prove that for non-geodesic such curves there exists a unique Frenet frame for which the original parameter is distinguished. Moreover, we obtain a necessary condition this Frenet frame to be a Cartan Frenet frame with respect to the original parameter. Examples of the considered curves are constructed.

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Authors and Affiliations

  1. Section of Mathematics and IT, Faculty of Pharmacy, Medical University of Plovdiv, 15-A Vasil Aprilov Blvd., Plovdiv, 4002, Bulgaria

    Hristo Manev

  2. Department of Algebra and Geometry, Faculty of Mathematics and Informatics, Paisii Hilendarski University of Plovdiv, 236 Bulgaria Blvd., Plovdiv, 4027, Bulgaria

    Hristo Manev

  3. Department of Algebra and Geometry, Faculty of Mathematics and Informatics, University of Veliko Tarnovo ”St. Cyril and St. Methodius”, 2 Teodosii Tarnovski Str., Veliko Tarnovo, 5003, Bulgaria

    Galia Nakova

Authors
  1. Hristo Manev
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  2. Galia Nakova
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Corresponding author

Correspondence to Galia Nakova.

Additional information

The Hristo Manev was partially supported by projects NI15-FMI-004 and MU15-FMIIT-008 of the Scientific Research Fund at the University of Plovdiv.

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Manev, H., Nakova, G. Slant Null Curves on Normal Almost Contact B-Metric 3-Manifolds with Parallel Reeb Vector Field. Results Math 71, 933–947 (2017). https://doi.org/10.1007/s00025-016-0535-x

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  • DOI: https://doi.org/10.1007/s00025-016-0535-x

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