Yamabe Solitons with potential vector field as torse forming

Yadab Chandra Mandal; Shyamal Kumar Hui

doi:10.4067/S0719-06462018000300037

DOI:

https://doi.org/10.4067/S0719-06462018000300037

Abstract

The Riemannian manifolds whose metric is Yamabe soliton with potential vector field as torse forming admitting Riemannian connection, semisymmetric metric connection and projective semisymmetric connection have been studied. An example is constructed to verify the theorem concerning Riemannian connection.

Keywords

Yamabe soliton , torse forming vector field , torqued vector field , semisymmetric metric connection , projective semisymmetric connection

Yadab Chandra Mandal Department of Mathematics, The University of Burdwan, Burdwan, 713104, West Bengal, India.
Shyamal Kumar Hui Department of Mathematics, The University of Burdwan, Burdwan, 713104, West Bengal, India.

Pages: 37–47
Date Published: 2019-03-15
Vol. 20 No. 3 (2018)

Barbosa, E. and Ribeiro, E., On conformal solutions of the Yamabe flow, Arch. Math., 101(2013), 79-89.

Chen, B. Y.,Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc., 52 (2015), 1535-1547.

Chen, B. Y.,Classification of torqued vector fields and its applications to Ricci solitons, Kragujevac J. of Math., 41(2) (2017), 239-250.

Friedmann, A. and Schouten, J. A., Uber die geometric derhalbsymmetrischen Ubertragung, Math. Zeitschr., 21 (1924), 211-223.

Hamilton, R. S.,The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., 71 (1988), 237-262.

Hamilton, R. S.,Lectures on geometric flows, unpublished manuscript, 1989.

Hayden, H. A.,Subspaces of space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.

Hui, S. K. and Chakraborty, D.,Ricci almost solitons on concircular Ricci pseudosymmetric Î²-Kenmotsu manifolds, Hacettepe J. of Math. and Stat., 47(3) (2018), 579-587.

Hui, S. K. and Mandal, Y. C., Yamabe solitons on Kenmotsu manifolds, Communications inKorean Math. Soc., (2018).

Mandal, Y. C. and Hui, S. K.,On the existence of Yamabe gradient solitons, Int. J. Math.Eng. Manag. Sci., 3(4) (2018), 491-497.

Shaikh, A. A. and Hui, S. K.,On extended generalized Ï†-recurrent Î²-Kenmotsu manifolds, Publ. De L‘ Inst. Math., 89(103) (2011), 77-88.

Shaikh, A. A. and Hui, S. K.,On pseudo cyclic Ricci symmetric manifolds admitting semisymmetric metric connection, Scientia series A: Math. Sci., 20 (2010), 73-80.

Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195-200.

Yano, K., On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo, 20(1944), 340-345.

Yano, K., On semi-symmetric metric connection, Rev. Roum. Math. Pures et Appl.(Bucharest), XV, 9, (1970), 1579-1586.

Yano, K. and Chen, B. Y., On the concurrent vector fields of immersed manifolds, KodaiMath. Sem. Rep., 23 (1971), 343-350.

Zhao, P.,Some properties of projective semisymmetric connections, Int. Math. Forum, 3(7)(2008), 341-347.