[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2021.61.4.813

Ricci-Yamabe Solitons and Gradient Ricci-Yamabe Solitons on Kenmotsu 3-manifolds

Sardar, Arpan (Department of Mathematics, University of Kalyani)
Sarkar, Avijit (Department of Mathematics, University of Kalyani)

Publication Information

Kyungpook Mathematical Journal / v.61, no.4, 2021 , pp. 813-822 More about this Journal

Abstract

The aim of this paper is to characterize a Kenmotsu 3-manifold whose metric is either a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton. Finally, we verify the obtained results by an example.

Keywords

Ricci-Yamabe soliton; Gradient Yamabe soliton; Kenmotsu manifolds; ${\eta}$ -paralle Ricci tensor; scalar curvature;

Citations & Related Records

Reference

1	D. E. Blair, Riemannian Geometry of contact and symplectic manifolds, Progress in Mathematics, 203(2010), Birkhauser, New work.
2	G. Catino and L. Mazzieri, Gradient Einstein solitons, Nonlinear Anal., 132(2016), 66-94. DOI
3	U. C. De and G. Pathak, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math., 35(2)(2004), 159-165.
4	D. Dey, Almost Kenmotsu metric as Ricci-Yamabe soliton, arXiv: 2005.02322v1[math.DG] 5 May, 2020.
5	S. Guler and M. Crasmareanu, Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy, Turkish J. Math., 43(5)(2019), 2631-2641. DOI
6	R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., 71(1998), 237-262. DOI
7	K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93-103. DOI
8	V. F. Kirichenko, On the geometry of Kenmotsu manifolds, Dokl. Akad. Nauk, 380(5)(2001), 585-587.
9	S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain structures which are closely related to almost contact structure, II, Tohoku Math. J., 13(1961), 281-294. DOI
10	Y. Wang, Yamabe soliton on 3-dimensional Kenmotsu manifolds, Bull. Belg. Math. Soc. Simon Stevin, 23(2016), 345-355. DOI
11	K. Yano, Concircular geometry. I. Concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195-200.
12	G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza and L. Mazzieri, The Ricci-Bourguignon flow, Pacific J. Math., 28(2017), 337-370. DOI
13	A. Ghosh, R. Sharma and J. T. Cho, Contact metric manifolds with η-parallel torsion tensor, Ann. Global Anal. Geom., 34(3)(2008), 287-299. DOI
14	R. S. Hamilton, Lectures on geometric flows, 1989 (unpublished).