Notes on Ricci solitons in $f$-cosymplectic manifolds
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 3, pp. 242-253 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The purpose of the article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classifications of $M$. We also give some properties of $f$-cosymplectic manifolds.
@article{JMAG_2017_13_3_a1,
     author = {Xiaomin Chen},
     title = {Notes on {Ricci} solitons in $f$-cosymplectic manifolds},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {242--253},
     year = {2017},
     volume = {13},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2017_13_3_a1/}
}
TY  - JOUR
AU  - Xiaomin Chen
TI  - Notes on Ricci solitons in $f$-cosymplectic manifolds
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2017
SP  - 242
EP  - 253
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2017_13_3_a1/
LA  - en
ID  - JMAG_2017_13_3_a1
ER  - 
%0 Journal Article
%A Xiaomin Chen
%T Notes on Ricci solitons in $f$-cosymplectic manifolds
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2017
%P 242-253
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2017_13_3_a1/
%G en
%F JMAG_2017_13_3_a1
Xiaomin Chen. Notes on Ricci solitons in $f$-cosymplectic manifolds. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 3, pp. 242-253. http://geodesic.mathdoc.fr/item/JMAG_2017_13_3_a1/

[1] N. Aktan, M. Yildirim, C. Murathan, “Almost $f$-Cosymplectic Manifolds”, Mediterr. J. Math., 11 (2014), 775–787 | DOI | MR | Zbl

[2] D.E. Blair, Rimemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203, Birkhäuser, Boston, 2002 | MR

[3] H.D. Cao, “Geometry of Ricci Solitons”, Chin. Ann. Math. Ser. B, 27 (2006), 141–162 | DOI | MR

[4] J.T. Cho, “Notes on Contact Ricci Solitons”, Proc. Edinb. Math. Soc., 54 (2011), 47–53 | DOI | MR | Zbl

[5] B. Chow, D. Knopf, The Ricci Flow: An Instruction, Mathematical Surveys and Monographs, 110, AMS, Providence, 2004 | DOI | MR

[6] S.I. Goldberg, K. Yano, “Integrability of Almost Cosymplectic Sstructure”, Pacific J. Math., 31 (1969), 373–382 | DOI | MR | Zbl

[7] A. Ghosh, “Kenmotsu 3-Metric as a Ricci Soliton”, Chaos Solitons Fractals, 44:8 (2011), 647–650 | DOI | MR | Zbl

[8] A. Ghosh, R. Sharma, “K-Contact Metrics as Ricci Solitons”, Beitr. Algebra Geom., 53 (2012), 25–30 | DOI | MR | Zbl

[9] A. Ghosh, R. Sharma, J.T. Cho, “Contact Metric Manifolds with $\eta$-Parallel Torsion Tensor”, Ann. Global. Anal. Geom., 31:3 (2008), 287–299 | DOI | MR

[10] R. Hamilton, “The Formation of Singularities in Ricci Flow”, Survey in Differential Geometry, v. 2, International Press, Cambridge, 1995, 7–136 | MR | Zbl

[11] K. Kenmotsu, “A Class of Contact Riemannian Manifold”, Tohoku Math. J., 24 (1972), 93–103 | DOI | MR | Zbl

[12] T.W. Kim, H.K. Pak, “Canonical Foliations of Certain Classes of Almost Contact Metric Structres”, Acta Math. Sin. (Engl. Ser.), 21:4 (2005), 841–846 | DOI | MR | Zbl

[13] O. Munteanu, N. Sesum, “On Gradient Ricci Solitons”, J. Geom. Anal., 23 (2013), 539–561 | DOI | MR | Zbl

[14] G. Perelman, The Entropy Formula for the Ricci Flow and its Geometric Applications, 39 pp., arXiv: math/0211159 [math.DG]

[15] H. Öztürk, N. Aktan, C. Murathan, Almost $\alpha$-Cosymplectic $(\kappa,\mu,\nu)$-Spaces, 24 pp., arXiv: 1007.0527v1 [math.DG]

[16] P. Petersen, W. Wylie, “Rigidity of Ggradient Ricci Solitons”, Pacific. J. Math., 241:2 (2009), 329–345 | DOI | MR | Zbl

[17] R. Sharma, “Certain Results on K-Contact and $(\kappa,\mu)$-Contact Manifolds”, J. Geom., 89 (2008) | DOI | MR

[18] K. Vaisman, “Conformal Changes of Almost Contact Metric Manifolds”, Lecture Notes in Mathematics, 792, Springer, Berlin, 1980, 435–443 | DOI | MR