Year 2020, Volume 8 , Issue 2, Pages 79 - 85 2020-10-15

A Note on Gradient $\ast$-Ricci Solitons

Krishnendu DE [1]


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 $\mathbb{H}^{2}(-4)\times \mathbb{R}$.                                                                                                                                 .                                                                      
$(k \mu)'$- almost Kenmotsu manifolds, $\ast$-Ricci solitons, gradient $\ast$-Ricci solitons
  • [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).
Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Orcid: 0000-0001-5264-5861
Author: Krishnendu DE (Primary Author)
Institution: kabi sukanta mahavidyalaya, Burdwan University
Country: India


Dates

Publication Date : October 15, 2020

Bibtex @research article { mathenot727083, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {79 - 85}, doi = {10.36753/mathenot.727083}, title = {A Note on Gradient \$\\ast\$-Ricci Solitons}, key = {cite}, author = {De, Krishnendu} }
APA De, K . (2020). A Note on Gradient $\ast$-Ricci Solitons . Mathematical Sciences and Applications E-Notes , 8 (2) , 79-85 . DOI: 10.36753/mathenot.727083
MLA De, K . "A Note on Gradient $\ast$-Ricci Solitons" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 79-85 <https://dergipark.org.tr/en/pub/mathenot/issue/57179/727083>
Chicago De, K . "A Note on Gradient $\ast$-Ricci Solitons". Mathematical Sciences and Applications E-Notes 8 (2020 ): 79-85
RIS TY - JOUR T1 - A Note on Gradient $\ast$-Ricci Solitons AU - Krishnendu De Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.727083 DO - 10.36753/mathenot.727083 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 79 EP - 85 VL - 8 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.727083 UR - https://doi.org/10.36753/mathenot.727083 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes A Note on Gradient $\ast$-Ricci Solitons %A Krishnendu De %T A Note on Gradient $\ast$-Ricci Solitons %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 2 %R doi: 10.36753/mathenot.727083 %U 10.36753/mathenot.727083
ISNAD De, Krishnendu . "A Note on Gradient $\ast$-Ricci Solitons". Mathematical Sciences and Applications E-Notes 8 / 2 (October 2020): 79-85 . https://doi.org/10.36753/mathenot.727083
AMA De K . A Note on Gradient $\ast$-Ricci Solitons. Math. Sci. Appl. E-Notes. 2020; 8(2): 79-85.
Vancouver De K . A Note on Gradient $\ast$-Ricci Solitons. Mathematical Sciences and Applications E-Notes. 2020; 8(2): 79-85.
IEEE K. De , "A Note on Gradient $\ast$-Ricci Solitons", Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, pp. 79-85, Oct. 2020, doi:10.36753/mathenot.727083