Research article

On constructing almost complex Norden metric structures

  • Received: 28 May 2022 Revised: 28 July 2022 Accepted: 28 July 2022 Published: 05 August 2022
  • MSC : 53B30, 53B35, 53D15

  • For a given almost contact Norden metric structure on a smooth manifold $ M $, one can obtain an almost complex Norden metric structure on $ M\times\mathbb{R} $. In this work, we study this construction in details and give the relations between the classes of these structures. Furthermore, we give examples of almost complex Norden metric structures of which the existence are guaranteed by the results of the paper.

    Citation: Mehmet Solgun. On constructing almost complex Norden metric structures[J]. AIMS Mathematics, 2022, 7(10): 17942-17953. doi: 10.3934/math.2022988

    Related Papers:

  • For a given almost contact Norden metric structure on a smooth manifold $ M $, one can obtain an almost complex Norden metric structure on $ M\times\mathbb{R} $. In this work, we study this construction in details and give the relations between the classes of these structures. Furthermore, we give examples of almost complex Norden metric structures of which the existence are guaranteed by the results of the paper.



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    [1] A. Gray, L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura. Appl., 123 (1980), 35–58. https://doi.org/10.1007/BF01796539 doi: 10.1007/BF01796539
    [2] D. Chinea, C. Gonzales, A classification of almost contact metric manifolds, Ann. Mat. Pur. Appl., 156 (1990), 15–36. https://doi.org/10.1007/BF01766972 doi: 10.1007/BF01766972
    [3] D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Switzerland: Birkhauser, 2002.
    [4] V. Alexiev, G. Ganchev, On the classification of the almost contact metric manifolds, Proc. 15th Spring Conf., 1986,155–161.
    [5] G. Ganchev, V. Mihova, K. Gribachev, Almost contact manifolds with B-metric, Math. Balkanica (N.S.), 7 (1993), 261–276.
    [6] G. Ganchev, A. Borisov, Note on the almost complex manifolds with a Norden metric, Compt. Rend. Acad. Bulg. Sci., 39 (1986), 31–34.
    [7] G. Nakova, S. Zamkovoy, Eleven classes of almost paracontact manifolds with semi-Riemannian metric of (n+1, n), P. Int. Colloq. Differ. Geom. Relat. F., 2010, 6–10.
    [8] J. A. Oubina, A classification for almost contact structures, Preprint, 1980.
    [9] M. Solgun, Y. Karababa, A natural way to construct an almost complex B-metric structure, Math. Meth. Appl. Sci., 44 (2021), 7607–7613. https://doi.org/10.1002/mma.6430 doi: 10.1002/mma.6430
    [10] M. Manev, Natural connection with totally skew-symmetric torsion on almost contactmanifolds with B-metric, Int. J. Geom. Methods Mod. Phys., 9 (2012), 20.
    [11] S. Ivanov, H. Manev, M. Manev, Sasaki-like almost contact complex Riemannian manifolds, J. Geom. Phys., 105 (2016), 136–148. https://doi.org/10.1016/j.geomphys.2016.05.009 doi: 10.1016/j.geomphys.2016.05.009
    [12] M. Manev, Ricci-like solitons on almost contact B-metric manifolds, J. Geom. Phys., 154 (2020), 103734. https://doi.org/10.1016/j.geomphys.2020.103734 doi: 10.1016/j.geomphys.2020.103734
    [13] M. Ivanova, L. Dospatliev, The components of the structure tensor of five-dimensional almost contact B-metric manifolds, Asian-Eur. J. Math., 13 (2020). https://doi.org/10.1142/S179355712050165X doi: 10.1142/S179355712050165X
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