On submanifolds of Kenmotsu manifold with Torqued vector field

Year 2020, , 843 - 853, 02.04.2020

Halil İbrahim Yoldaş , Şemsi Eken Meriç Erol Yaşar

https://doi.org/10.15672/hujms.479184

Cited By: 3

Abstract

In this paper, we consider the submanifold $M$ of a Kenmotsu manifold $\tilde M$ endowed with torqued vector field $\mathcal{T}$. Also, we study the submanifold $M$ admitting a Ricci soliton of both Kenmotsu manifold $\tilde M$ and Kenmotsu space form $\tilde M(c)$. Indeed, we provide some necessary conditions for which such a submanifold $M$ is an $\eta-$Einstein. We have presented some related results and classified. Finally, we obtain an important characterization which classifies the submanifold $M$ admitting a Ricci soliton of Kenmotsu space form $\tilde M(c)$.

Keywords

Kenmotsu manifold, Ricci soliton, Torqued vector field

References

• [1] C. S. Bagewadi, and G. Ingalahalli, Ricci Solitons in Lorentzian α−Sasakian Manifolds, Acta Math. Acad. Paedagog. Nyházi. (N.S), 28 (1), 59-68, 2012.
• [2] C. L. Bejan and M. Crasmareanu, Second Order Parallel Tensors and Ricci Solitons in 3-Dimensional Normal Paracontact Geometry, Ann. Glob. Anal. Geom., 46 , 117- 127, 2014.
• [3] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, 509, Springer-Verlag, Berlin, 1976.
• [4] B.-Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.
• [5] B.-Y. Chen, Some Results on Concircular Vector Fields and Their Applications to Ricci Solitons, Bull. Korean Math. Soc., 52 (5), 1535-1547, 2015.
• [6] B.-Y. Chen, Rectifying Submanifolds of Riemannian Manifolds and Torqued Vector Fields, Kragujevac J. Math., 41 (1), 93-103, 2017.
• [7] B.-Y. Chen, Classification of Torqued Vector Fields and Its Applications to Ricci Solitons, Kragujevac J. Math., 41 (2), 239-250, 2017.
• [8] J. T. Cho and J. Park, Gradient Ricci Solitons with Semi-Symmetry, Bull. Korean Math. Soc., 51 (1), 213-219, 2014.
• [9] A. Ghosh, Certain Contact Metrics as Ricci Almost Solitons, Results Maths., 65, 81-94, 2014.
• [10] A. Ghosh, Kenmotsu 3-Metric as a Ricci Soliton, Chaos, Solitons & Fractals, 44 (8), 647-650, 2011.
• [11] R. S. Hamilton, Three-Manifolds with Positive Ricci Curvature, J. Diff. Geom., 17 (2), 255-306, 1982.
• [12] R. S. Hamilton, The Ricci Flow on Surfaces, Mathematics and General Relativity (Santa Cruz, CA, 1986), Contemp. Math., A.M.S, 71, 237-262, 1988.
• [13] S. K. Hui, S. K. Yadav and A. Patra, Almost Conformal Ricci Solitons on f−Kenmotsu Manifolds, Khayyam J. Math., 5 (1), 89-104, 2019.
• [14] J.-B. Jun, U. C. De and G. Pathak, On Kenmotsu Manifolds, J. Korean Math. Soc., 42 (3), 435-445, 2005.
• [15] K. Kenmotsu, A Class of Almost Contact Riemannian Manifolds, Tohoku Math. J., 24, 93-103, 1972.
• [16] H. G. Nagaraja and C. R. Premalatha, Ricci Solitons in Kenmotsu Manifolds, J. Math. Anal., 3 (2), 18-24, 2012.
• [17] S. Y. Perktaş and S. Keleş, Ricci Solitons in 3-Dimensional Normal Almost Paracontact Metric Manifolds, Int. Electron. J. Geom., 8 (2), 34-45, 2015.
• [18] R. Sharma, Certain Results on K-Contact and (k, μ)−Contact Manifolds, J. Geom., 89, (1-2), 138-147, 2008.
• [19] R. Sharma and A. Ghosh, Sasakian 3-Manifolds as a Ricci Soliton Represents the Heisenberg Group, Int. J. Geom. Methods Mod. Phys, 8 (1), 149-154., 2011.
• [20] S. Sular and C. Özgür, On Some Submanifolds of Kenmotsu Manifolds, Chaos, Solitons & Fractals, 4 (2), 1990-1995, 2009.
• [21] M. M. Tripathi, Ricci Solitons in Contact Metric Manifolds, arXiv:0801.4222v1, [math DG], 2008.
• [22] K. Yano and M. Kon, Structures on Manifolds, Series in Mathematics, World Scientific Publishing, Springer, 1984.
• [23] H. İ. Yoldaş, Ş. E. Meriç, E. Yaşar, On Generic Submanifold of Sasakian Manifold with Concurrent Vector Field, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (2), 1983-1994, 2019.