A Note on Gradient ∗-Ricci Solitons
In the offering exposition we characterize (k, µ) 0- almost Kenmotsu 3-manifolds admitting gradient ∗-Ricci soliton. It is shown that in a (k, µ)0 - almost Kenmotsu manifold with k < −1 admitting a gradient ∗-Ricci soliton, either the soliton is steady or the manifold is locally isometric to a rigid gradient Ricci soliton H2(−4) × R.
___
[1] Blaga, A.M.: η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat 30 , 489–496(2016).[2] Blaga, A.M.: η-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.: ∗-Ricci soliton on (k, µ)0 -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.: ∗-Ricci Soliton within the framework of Sasakian and (k, µ)-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 ∗-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.: ∗-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.: ∗-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 ∗-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)
- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -
Sayıdaki Diğer Makaleler
Internal Categories in Crossed Semimodules and Schreier Internal Categories
Sibel ACIK KEMALOĞLU, Mehmet YILMAZ
On Crossed Squares of Commutative Algebras
Koray Yılmaz, Elis Soylu Yılmaz
On the Pasting Lemma on a Fuzzy Soft Topological Space with Mixed Structure