D-Homothetic Deformations and Almost Paracontact Metric Manifolds

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.

Keywords

• Almost paracontact metric structure
• D-homothetic deformation
• Killing vector field

References

1. [1] Blair D.E., D-homothetic warping, Publications de l’Institut Mathematique, 94(108), 47-54, 2013.
2. [2] Bulut Ş., D-homothetic deformation on almost contact B-metric manifolds, Journal of Geometry, 110(2), 1-12, 2019.
3. [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. [4] Dixmier J., Sur les repr ´esentations unitaires des groupes de Lie nilpotentes III, Canadian Journal of Mathematics, 10, 321-348, 1958.
5. [5] Kaneyuki S., Williams F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Mathematical Journal, 99, 173-187, 1985.
6. [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. [7] Nakova G., Zamkovoy S., Almost paracontact manifolds, arXiv:0806.3859v2 [math.DG], 2009.
8. [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. [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. [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. [11] Zamkovoy S., Canonical connections on paracontact manifolds, Annals of Global Analysis and Geometry, 36(37), 2009.
12. [12] Zamkovoy S., On para-Kenmotsu manifolds, Filomat, 32(14), 4971-4980, 2018.
13. [13] Zamkovoy S., Nakova G., The decomposition of almost paracontact metric manifolds in eleven classes revisited, Journal of Geometry, 109(1), 1-23, 2018.