Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection
Abstract
The following research investigates various types of soliton of NC (Nearly Cosymplectic) manifolds with SVK (Schouten-van Kampen) connections, which are steady, shrinking, or expanding. Further, we investigate the geometric characteristics of Ricci solitons, Yamabe solitons, $\eta$-ricci soliton etc. We also study the curvature features of the SVK connection on an NC manifold. In addition, an example is developed to demonstrate the results.
Keywords
Einstein manifold, Nearly cosymplectic manifold, Quasi Einstein manifold, Ricci soliton, Schouten van Kampen connection, Yamabe soliton
Project Number
DST/WISE-PhD/PM/2023/6(G)
Thanks
The author acknowledges the Department of Science & Technology, Government of India, for financial support vide reference no DST/WISE-PhD/PM/2023/6(Gunder 'WISE FELLOWSHIP for Ph.D.' to carry out this work.
References
- [1] A. Bejancu, H. R. Farran, Foliations and Geometric Structures, Springer Science and Business Media, (580) (2006).
- [2] A. Dündar, N. Aktan, Some results on nearly cosymplectic manifolds, Univ. J. Math. Appl., 2(4) (2019), 218-223.
- [3] R. Kundu, A. Das, A. Biswas, Conformal Ricci soliton in Sasakian manifolds admitting general connection, J. Hyperstruct., 13(1) (2024), 46-61.
- [4] S. Sundriyal, J. Upreti, Solitons on Para-Sasakian manifold with respect to the Schouten-Van Kampen connection, Ganita Vol., 73(1) (2023), 25-33.
- [5] A. Yıldız, f-Kenmotsu manifolds with the Schouten-Van Kampen connection, Publications de l’Institut Mathematique, 102(116) (2017), 93-105.
- [6] G. Ghosh, On Schouten-Van Kampen connection in Sasakian manifolds, Boletim da Sociedade Paranaense de Mathematica, 36 (2018), 171-182.
- [7] M. Altunbaş, Some characterizations of hyperbolic Ricci solitons on nearly cosymplectic manifolds with respect to the Tanaka-Webster connection, Istanbul J. Math., 2(1) (2024), 28-32.
- [8] D. Blair, Almost contact manifolds with Killing structure tensors, Pacific J. Math., 39(2) (1971), 285-292.
- [9] J. T. Cho, M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tˆohoku Math. J., Second Series, 61(2) (2009), 205-212.
- [10] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17(2) (1982), 255-306.
