D-Homothetic Deformations and Almost Paracontact Metric Manifolds

Year 2024, Volume: 5 Issue: 1, 1 - 14, 31.01.2024

Şirin Aktay

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.

Keywords

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

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.