Pseudosymmetric normal paracontact metric space forms admitting (α, β)− type almost η−Ricci-Yamabe solitons

  • Tuğba Mert Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140 Sivas, Turkey
  • Mehmet Atçeken Department of Mathematics, Faculty of Arts and Sciences, Aksaray University, 68100 Aksaray, Turkey
Ariticle ID: 231
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Keywords: ricci-pseudosymmetric manifold; η−Ricci-Yamabe soliton; normal paracontact metric space form

Abstract

In this paper, we have considered normal paracontact metric space forms ad- mitting (α, β) −type almost η−Ricci-Yamabe solitons by means of some curvature ten- sors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admit- ting (α, β) −type almost η−Ricci-Yamabe soliton have introduced according to choos- ing of some special curvature tensors such as Riemann, concircular, projective, W1 curvature tensor. After that, according to choosing of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting (α, β) −type almost η−Ricci-Yamabe soliton to be Ricci semisymmetric. Then some characteriza- tions are obtained and some classifications are made under the some conditions.

References

[1] Hamilton RS. The Ricci flow on surfaces, Mathematics and general relativity. Contemporary Mathematics. 1988, 71: 237–262.

[2] Güler S, Crasmareanu M. Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy. Turkey Journal Mathematics 2019, 43: 2631–2641.

[3] Catino G, Cremaschi L, Djjadli Z, et al. The Ricci-Bourguignon flow. Pacific Journal Mathematics. 2017, 287: 337– 370.

[4] Dey D. Almost enmotsumetrics as Ricci-Yamabe soliton. arXiv. 2005: arxiv:2020.02322.

[5] Siddiqi MD, Akyol MA. η-Ricci-Yamabe soliton on Riemannian submersions from Riemannian manifolds. arxiv. 2020: arXiv:2004.14124.

[6] Cho JT, Kimura M. Ricci solitons and real hypersurfaces in a complex space form. Tohoku Mathematics Journal. 2009, 61(2): 205–212.

[7] Blaga AM. η−Ricci solitons on para-Kenmotsu manifolds. Balkan Journal of Geometry and its Applications. 2015, 20(1): 1–13.

[8] Blaga AM. On gradient η−Einstein solitons. Kragujevac Journal Mathematics. 2018, 42(2): 229–237.

[9] Chen BY. Deshmukh S. Yamabe and quasi-Yamabe soliton on Euclidean submanifolds. Mediterranean Journal of Mathematics. 2018, 15: 194.

[10] Crasmareanu M. A new Approach to gradient Ricci solitons and Generalizations. Filomat. 2018, 32(9): 3337–3346.

[11] Güler S. On a Class of Gradient Almost Ricci Solitons. Bulletin of the Malaysian Mathematical Sciences Society. 2020, 43: 3635–3650.

[12] Kenayuki S, Williams FL. Almost paracontact and parahodge structures on manifolds. Nagoya Mathematics Jourrnal. 1985, 99: 173–187.

[13] Zamkovoy S. Canonical connections on paracontact manifolds. Annals of Globel Analysis and Geometry. 2009, 36: 37–60.

[14] Welyczko J. On Legendre curvaes in 3-dimensional normal almost paracontact metric manifolds. Result Mathematics. 2009, 54: 377–387.

[15] Welyczko J. Slant curves in 3-dimensional normal contact metric manifolds. Mediterranean Journal of Mathematics. 2014, 11: 965–978.

[16] Pandey HB, Kumar A. Anti invariant submanifolds of almost paracontact metric manifolds. Indian Journal of Pure and Applied Mathematics. 1985, 16(6): 586–590.

[17] Yıldırım Ü, Atçeken M, Dirik S. A normal paracontact metric manifold satisfying some conditions on the M- projectivecurvature tensor. Konuralp Journal of Mathematics. 2019, 7(1): 217–221.

[18] Yıldırım Ü, Atçeken M, Dirik S. Pseudo projective curvture tensor satisfying some properties on a normal paracon- tactmetric manifold. Communication Factually Science University. 2019, 68(1): 997–1006.

Published
2024-04-01
How to Cite
Mert, T., & Atçeken, M. (2024). Pseudosymmetric normal paracontact metric space forms admitting (α, β)− type almost η−Ricci-Yamabe solitons. Journal of AppliedMath, 2(2), 231. https://doi.org/10.59400/jam.v2i2.231
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Article