Research Article
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D-Homothetic Deformations and Almost Paracontact Metric Manifolds

Year 2024, , 1 - 14, 31.01.2024
https://doi.org/10.54974/fcmathsci.1240849

Abstract

In this study, we determine some of the classes of almost paracontact metric structures which are invariant under D-homothetic deformations. We write the Riemannian curvature tensor, the Ricci tensor and the scalar curvature when the characteristic vector field is Killing. In addition, we give examples.

Supporting Institution

Eskişehir Technical University

Project Number

22 ADP 011

References

  • [1] Blair D.E., D-homothetic warping, Publications de l’Institut Mathematique, 94(108), 47-54, 2013.
  • [2] Bulut Ş., D-homothetic deformation on almost contact B-metric manifolds, Journal of Geometry, 110(2), 1-12, 2019.
  • [3] De U.C., Ghosh S., D-homothetic deformation of normal almost contact metric manifolds, Ukrains’kyi Matematychnyi Zhurnal, 64(10), 1330-1329, 2012.
  • [4] Dixmier J., Sur les repr ´esentations unitaires des groupes de Lie nilpotentes III, Canadian Journal of Mathematics, 10, 321-348, 1958.
  • [5] Kaneyuki S., Williams F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Mathematical Journal, 99, 173-187, 1985.
  • [6] Kocabaş Ü., Aktay Ş., Examples of almost para-contact metric structures on 5-dimensions, Fundamental Journal of Mathematics and Applications, 5(2), 89-97, 2022.
  • [7] Nakova G., Zamkovoy S., Almost paracontact manifolds, arXiv:0806.3859v2 [math.DG], 2009.
  • [8] Özdemir N., Solgun M., Aktay Ş., Almost paracontact metric structures on 5-dimensional nilpotent Lie algebras, Fundamental Journal of Mathematics and Applications, 3(2), 175-184, 2020.
  • [9] Özdemir N., Aktay Ş., Solgun M., Almost paracontact structures obtained from G∗2(2) structures, Turkish Journal of Mathematics, 42, 3025-3022, 2018.
  • [10] Solgun, M., Some results on D-homothetic deformation on almost paracontact metric manifolds, Fundamental Journal of Mathematics and Applications, 4(4), 264-270, 2021.
  • [11] Zamkovoy S., Canonical connections on paracontact manifolds, Annals of Global Analysis and Geometry, 36(37), 2009.
  • [12] Zamkovoy S., On para-Kenmotsu manifolds, Filomat, 32(14), 4971-4980, 2018.
  • [13] Zamkovoy S., Nakova G., The decomposition of almost paracontact metric manifolds in eleven classes revisited, Journal of Geometry, 109(1), 1-23, 2018.
Year 2024, , 1 - 14, 31.01.2024
https://doi.org/10.54974/fcmathsci.1240849

Abstract

Project Number

22 ADP 011

References

  • [1] Blair D.E., D-homothetic warping, Publications de l’Institut Mathematique, 94(108), 47-54, 2013.
  • [2] Bulut Ş., D-homothetic deformation on almost contact B-metric manifolds, Journal of Geometry, 110(2), 1-12, 2019.
  • [3] De U.C., Ghosh S., D-homothetic deformation of normal almost contact metric manifolds, Ukrains’kyi Matematychnyi Zhurnal, 64(10), 1330-1329, 2012.
  • [4] Dixmier J., Sur les repr ´esentations unitaires des groupes de Lie nilpotentes III, Canadian Journal of Mathematics, 10, 321-348, 1958.
  • [5] Kaneyuki S., Williams F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Mathematical Journal, 99, 173-187, 1985.
  • [6] Kocabaş Ü., Aktay Ş., Examples of almost para-contact metric structures on 5-dimensions, Fundamental Journal of Mathematics and Applications, 5(2), 89-97, 2022.
  • [7] Nakova G., Zamkovoy S., Almost paracontact manifolds, arXiv:0806.3859v2 [math.DG], 2009.
  • [8] Özdemir N., Solgun M., Aktay Ş., Almost paracontact metric structures on 5-dimensional nilpotent Lie algebras, Fundamental Journal of Mathematics and Applications, 3(2), 175-184, 2020.
  • [9] Özdemir N., Aktay Ş., Solgun M., Almost paracontact structures obtained from G∗2(2) structures, Turkish Journal of Mathematics, 42, 3025-3022, 2018.
  • [10] Solgun, M., Some results on D-homothetic deformation on almost paracontact metric manifolds, Fundamental Journal of Mathematics and Applications, 4(4), 264-270, 2021.
  • [11] Zamkovoy S., Canonical connections on paracontact manifolds, Annals of Global Analysis and Geometry, 36(37), 2009.
  • [12] Zamkovoy S., On para-Kenmotsu manifolds, Filomat, 32(14), 4971-4980, 2018.
  • [13] Zamkovoy S., Nakova G., The decomposition of almost paracontact metric manifolds in eleven classes revisited, Journal of Geometry, 109(1), 1-23, 2018.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Şirin Aktay 0000-0003-2792-3481

Project Number 22 ADP 011
Publication Date January 31, 2024
Published in Issue Year 2024

Cite

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.