A Note on Gradient $\ast$-Ricci Solitons

In the offering exposition we characterize $(k,\mu)'$- almost Kenmotsu $3$-manifolds admitting gradient $\ast$-Ricci soliton. It is shown that a $(k,\mu)'$- almost Kenmotsu manifold with $k<-1$ is admitting a gradient $\ast$-Ricci soliton, either the soliton is steady or the manifold is locally isometric to a rigid gradient Ricci soliton $\mathbb{H}^{2}(-4)\times \mathbb{R}$. .

Keywords:

$(k \mu)'$- almost Kenmotsu manifolds, $\ast$-Ricci solitons gradient $\ast$-Ricci solitons,

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[1] Blaga, A.M.: $\eta$-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat 30 , 489–496(2016).
[2] Blaga, A.M.: $\eta$-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl. 20 , 1–13(2015).
[3] Blair, D.E.: Contact manifold in Riemannian geometry. Lecture Notes on Mathematics, Springer, Berlin, 509,(1976).
[4] Blair, D.E.: Riemannian geometry on contact and symplectic manifolds, Progr. Math., 203, Birkhäuser, (2010).
[5] Blair, D.E.: Koufogiorgos, T., Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel. J. Math. 91, 189–214(1995).
[6] Dai, X., Zhao,Y., De, U.C.: $\eta$-Ricci soliton on $(k; \mu)'$-almost Kenmotsu manifolds, Open Math. 17 , 874-882(2019).
[7] Dileo, G., Pastore, A.M.: Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93, 46–61(2009).
[8] Duggal, K. L.: Almost Ricci Solitons and Physical Applications, Int. El. J. Geom. 2 , 1–10(2017).
[9] Ghosh, A., Patra, D.S.: $\eta$-Ricci Soliton within the framework of Sasakian and (k; )-contact manifold, Int. J. Geom. Methods Mod. Phys. 15 (7) 1850120 (2018).
[10] Gray, A.: Spaces of constancy of curvature operators, Proc. Amer. Math. Soc., 17, 897–902(1966).
[11] Hamada, T.: Real Hypersurfaces of Complex Space Forms in Terms of Ricci $\eta$-Tensor, Tokyo J. Math. 25 , 473– 483(2002).
[12] Hamilton, R. S.: The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz, CA, 1986), 237–262, Contemp. Math. 71, American Math. Soc., (1988).
[13] Kaimakamis, G., Panagiotidou, K.: $\eta$-Ricci solitons of real hypersurfaces in non-flat complex space forms, J. Geom. and Phys. 86 , 408–413(2014).
[14] Majhi, P., De, U. C., Suh, Y. J.: $\eta$-Ricci solitons and Sasakian 3-manifolds, Publ. Math. Debrecen 93 , 241–252(2018).
[15] Petersen, P., Wylie, W.: Rigidity of gradient Ricci solitons, Pacific J. Math. 241, 329–345(2009).
[16] Petersen, P., Wylie,W.: On gradient Ricci solitons with symmetry, Proc. Amer. Math. Soc. 137, 2085–2092(2009).
[17] Pigola, S., Rigoli, M. Rimoldi,M., Setti, A.: Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci. 10, 757–799(2011).
[18] Prakasha, D.G., Veeresha, P.: Para-Sasakian manifolds and $\eta$-Ricci solitons, arXiv:1801.01727v1.
[19] Tachibana, S.: On almost-analytic vectors in almost-Kählerian manifolds, Tohoku Math. J. 11 , 247–265(1959).
[20] Tanno, S.: Some differential equations on Riemannian manifolds, J. Math. Soc. Japan, 30, 509–531(1978).

Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

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