Conformal Ricci soliton in Sasakian manifolds admitting general connection

Document Type : Research Paper

Authors

1 Department of Mathematics, Raiganj University of Uttar Dinajpur, P.O.Box Raiganj, Raiganj, India

2 Mathabhanga College

Abstract

The object of the present paper is to study the Conformal Ricci soliton in Sasakian manifold admitting general connection, which is induced with quarter symmetric metric connection, generalized Tanaka Webster connection, Schouten-Van Kampen connection and Zamkovoy connection. Furthermore, we study CG-semi symmetric and CG-semi symmetric Sasakian manifolds admitting Conformal Ricci Soliton.

Keywords

Main Subjects


[1] N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Kenmotsu manifold, Global Journal of Advanced Research on Classical and Modern Geometries, 4(1)(2015), 15-21.
[2] A. E. Fischer, An Introduction to Conformal Ricci  ow, Classical and Quantum Gravity, 21(3)(2004), S171-S218.
[3] A. Biswas, S. Das and K.K. Baishya, On Sasakian manifolds satisfying curvature restrictions with respect to quarter symmetric metric connection, Scientific Studies and Research Series Mathematics and Informatics, 28(1) (2018), 29-40.
[4] A. Biswas and K. K. Baishya, Study on generalized pseudo (Ricci) symmetric Sasakian manifold admitting general connection, Bulletin of the Transilvania University of Brasov, 12(2)(2019), 233-246.
[5] A. Biswas and K.K. Baishya, A general connection on Sasakian manifolds and the case of almost pseudo symmetric Sasakian manifolds, Scienti c Studies and Research Series Mathematics and Informatics, 29(1)(2019), 59-72.
[6] R. S. Hamilton, The Ricci  ow on surfaces, Mathematics and general relativity, Contemp. Math., 71(1988), 237-261.
[7] S. Sasaki, Lectures Notes on Almost Contact Manifolds, Part I, Tohoku University (1975).
[8] J. A. Schouten and E. R. Van Kampen, Zur Einbettungs-und Krummungstheorie nichtholonomer Gebilde, Math. Ann., 103(1930), 752-783, (1930).
[9] S. Tanno, The automorphism groups of almost contact Riemannian manifold, Tohoku Math. J., 21(1969), 21-38.
[10] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(1)(2008), 37-60.
[11] K. Yano and M. Kon, Structures on manifolds, World Scienti c Publishing Co1984, 41, Acad. Bucharest, 2008, 249-308.
[12] K.Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.
[13] L. P. Eisenhart, Riemannian Geometry, Princeton University Press, 1949.
[14] S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
[15] G. Perelman, The entropy formula for the Ricci  ow and its geometric applications, http://arXiv.org/abs/math/0211159, 2002, 1-39.
[16] G. Perelman, Ricci  ow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, 2003, 1-22.