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Some Inequalities for Ricci Solitons

Year 2018, Volume: 10, 160 - 164, 29.12.2018

Abstract

We deal with a submanifold of a Ricci soliton $(\bar{M},\bar{g},V,\lambda)$ and obtain
that under what conditions such a submanifold is Ricci soliton. Moreover, we establish some inequalities for Ricci solitons to obtain the relationships between the intrinsic or extrinsic invariants.

References

  • Barros, A, Vieira Gomes, JN, Ribeiro, E. \emph{Immersion of almost Ricci solitons into a Riemannian manifold }, Math. Cont. \textbf{40}(2011), 91--102. Bejan, C.L., Crasmareanu, M., \emph{Ricci solitons in manifolds with quasi-constant curvature}, Publ. Math. Debrecen. \textbf{78}(2011), 235--243. Bejan, C.L., Crasmareanu, M., \emph{Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry}, Anal. Glob. Anal. Geom. \textbf{46}(2014), 117--128. Blaga, A.M., Perkta\c{s}, S.Y., \emph{Remarks on almost $\eta-$Ricci solitons in ($\varepsilon$)-para Sasakian manifolds}, (2018), arXiv:1804.05389v1. Blaga, A.M., Perkta\c{s}, S.Y, Acet, B.E., Erdo\u{g}an, F.E., \emph{$\eta-$Ricci solitons in ($\varepsilon$)-almost paracontact metric manifolds}, (2017), arXiv: 1707.07528v2. Calin, C., Crasmareanu, M., \emph{From the Eisenhart problem to Ricci solitons in $f$-Kenmotsu manifolds}, Bull. Malays. Math. Sci. Soc. \textbf{33}(2010), 361--368. Besse, A.L., Einstein manifolds, Berlin-Heidelberg-New York: Spinger-Verlag, 1987. Chen, B.Y., \emph{Concircular vector fields and pseudo-K\"{a}hler manifolds}, Kragujevac J. Math. \textbf{40}(2016), 7--14. Chen B.Y., Deshmukh, S., \emph{Ricci solitons and concurrent vector Field}, Balkan J. Geom. Its Appl. \textbf{20}(2015), 14--25. Chen, B.Y., \emph{Ricci solitons on Riemannian submanifolds}. In: Mihai A, Mihai I, editors. RIGA-Proceedings of the Conference; 19-21 May; Bucharest, Romania. University of Bucharest Press, (2014) 30--45. Chen, B.Y., Deshmukh, S., \emph{Classification of Ricci solitons on Euclidean hypersurfaces}, Int. J. Math. \textbf{ 25}(2014), 22 pp. Hamilton, R.S., \emph{The Ricci flow on surfaces, Mathematics and General Relativity(Santa Cruz, CA, 1986)}, Contemp. Math. Amer. Math. Soc. \textbf{71}(1988), 237--262. Perelman, G., \emph{The Entropy formula for the Ricci flow and its geometric applications}, (2002) arXiv math/0211159. Tripathi, M.M., \emph{Certain basic inequalities for submanifolds in $(\kappa,\mu)$ -space}, Recent advances in Riemannian and Lorentzian geometries, Baltimore: MD, 2003. Deshmukh, S., Alodan, H., Al-Sodais, H., \emph{A note on Ricci solitons}, Balkan J. Geom. Its Appl. 16(2011) 48--55. Perkta\c{s}, S.Y., Kele\c{s}, S., \emph{Ricci solitons in 3-dimensional normal almost paracontact metric manifolds}, Int. Elect. J. Geom. 8(2015), 34--45.
Year 2018, Volume: 10, 160 - 164, 29.12.2018

Abstract

References

  • Barros, A, Vieira Gomes, JN, Ribeiro, E. \emph{Immersion of almost Ricci solitons into a Riemannian manifold }, Math. Cont. \textbf{40}(2011), 91--102. Bejan, C.L., Crasmareanu, M., \emph{Ricci solitons in manifolds with quasi-constant curvature}, Publ. Math. Debrecen. \textbf{78}(2011), 235--243. Bejan, C.L., Crasmareanu, M., \emph{Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry}, Anal. Glob. Anal. Geom. \textbf{46}(2014), 117--128. Blaga, A.M., Perkta\c{s}, S.Y., \emph{Remarks on almost $\eta-$Ricci solitons in ($\varepsilon$)-para Sasakian manifolds}, (2018), arXiv:1804.05389v1. Blaga, A.M., Perkta\c{s}, S.Y, Acet, B.E., Erdo\u{g}an, F.E., \emph{$\eta-$Ricci solitons in ($\varepsilon$)-almost paracontact metric manifolds}, (2017), arXiv: 1707.07528v2. Calin, C., Crasmareanu, M., \emph{From the Eisenhart problem to Ricci solitons in $f$-Kenmotsu manifolds}, Bull. Malays. Math. Sci. Soc. \textbf{33}(2010), 361--368. Besse, A.L., Einstein manifolds, Berlin-Heidelberg-New York: Spinger-Verlag, 1987. Chen, B.Y., \emph{Concircular vector fields and pseudo-K\"{a}hler manifolds}, Kragujevac J. Math. \textbf{40}(2016), 7--14. Chen B.Y., Deshmukh, S., \emph{Ricci solitons and concurrent vector Field}, Balkan J. Geom. Its Appl. \textbf{20}(2015), 14--25. Chen, B.Y., \emph{Ricci solitons on Riemannian submanifolds}. In: Mihai A, Mihai I, editors. RIGA-Proceedings of the Conference; 19-21 May; Bucharest, Romania. University of Bucharest Press, (2014) 30--45. Chen, B.Y., Deshmukh, S., \emph{Classification of Ricci solitons on Euclidean hypersurfaces}, Int. J. Math. \textbf{ 25}(2014), 22 pp. Hamilton, R.S., \emph{The Ricci flow on surfaces, Mathematics and General Relativity(Santa Cruz, CA, 1986)}, Contemp. Math. Amer. Math. Soc. \textbf{71}(1988), 237--262. Perelman, G., \emph{The Entropy formula for the Ricci flow and its geometric applications}, (2002) arXiv math/0211159. Tripathi, M.M., \emph{Certain basic inequalities for submanifolds in $(\kappa,\mu)$ -space}, Recent advances in Riemannian and Lorentzian geometries, Baltimore: MD, 2003. Deshmukh, S., Alodan, H., Al-Sodais, H., \emph{A note on Ricci solitons}, Balkan J. Geom. Its Appl. 16(2011) 48--55. Perkta\c{s}, S.Y., Kele\c{s}, S., \emph{Ricci solitons in 3-dimensional normal almost paracontact metric manifolds}, Int. Elect. J. Geom. 8(2015), 34--45.
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Details

Primary Language English
Journal Section Articles
Authors

Şemsi Eken Meriç

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Eken Meriç, Ş. (2018). Some Inequalities for Ricci Solitons. Turkish Journal of Mathematics and Computer Science, 10, 160-164.
AMA Eken Meriç Ş. Some Inequalities for Ricci Solitons. TJMCS. December 2018;10:160-164.
Chicago Eken Meriç, Şemsi. “Some Inequalities for Ricci Solitons”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 160-64.
EndNote Eken Meriç Ş (December 1, 2018) Some Inequalities for Ricci Solitons. Turkish Journal of Mathematics and Computer Science 10 160–164.
IEEE Ş. Eken Meriç, “Some Inequalities for Ricci Solitons”, TJMCS, vol. 10, pp. 160–164, 2018.
ISNAD Eken Meriç, Şemsi. “Some Inequalities for Ricci Solitons”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 160-164.
JAMA Eken Meriç Ş. Some Inequalities for Ricci Solitons. TJMCS. 2018;10:160–164.
MLA Eken Meriç, Şemsi. “Some Inequalities for Ricci Solitons”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 160-4.
Vancouver Eken Meriç Ş. Some Inequalities for Ricci Solitons. TJMCS. 2018;10:160-4.