Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T14:46:26.239Z Has data issue: false hasContentIssue false
  • English
  • Français

RICCI SOLITONS AND CONTACT METRIC MANIFOLDS

Published online by Cambridge University Press:  02 August 2012

AMALENDU GHOSH
AMALENDU GHOSH*
Affiliation:
Department of Mathematics, Krishnagar Government College, Krishnagar 741101, West Bengal, India e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study on a contact metric manifold M2n+1(ϕ, ξ, η, g) such that g is a Ricci soliton with potential vector field V collinear with ξ at each point under different curvature conditions: (i) M is of pointwise constant ξ-sectional curvature, (ii) M is conformally flat.

Keywords

53C1553C2553D10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 123 - 130
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Blair, D. E., Riemannian geometry of contact and symplectic manifolds in Progress in Mathematics, vol. 203 (Bass, H., Oesterle, J. and Weinstein, A. Editors) (Birkhauser, Basel, Switzerland, 2002).Google Scholar
2.Blair, D. E. and Koufogiorgos, T., When is the tangent sphere bundle conformally flat?, J. Geom. 49 (1994), 55–66.CrossRefGoogle Scholar
3.Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189–214.Google Scholar
4.Blair, D. E. and Sharma, R., Generalization of Myers' theorem on a contact manifold, Illinois J. Math. 34 (1990), 837–844.Google Scholar
5.Boyer, C. P. and Galicki, K., Einstein manifolds and contact geometry, Proc. Am. Math. Soc. 129 (2001), 2419–2430.CrossRefGoogle Scholar
6.Cao, H.-D. and Zhu, X.-P., A complete proof of the Poincare and geometrization conjectures-application of the Hamilton–Perelman theory of the Ricci flow, Asian J. Math. 10 (2006), 165–492.Google Scholar
7.Cho, J. T., Notes on contact Ricci solitons, Proc. Edin. Math. Soc. 54 (2011), 47–53.Google Scholar
8.Cho, J. T. and Sharma, R., Contact geometry and Ricci solitons, Int. J. Geom. Methods Math. Phys. 7 (2010), 951–960.CrossRefGoogle Scholar
9.Chow, B. and Knopf, D., The Ricci flow: An introduction, mathematical surveys and monographs, Am. Math. Soc. 110 (2004).Google Scholar
10.Ghosh, A., Certain results of real hypersurfaces in a complex space form, Glasgow Math. J (2011) (published online 2 August).Google Scholar
11.Ghosh, A., Koufogiorgos, T. and Sharma, R., Conformally flat contact metric manifolds, J. Geom. 70 (2001), 66–76.CrossRefGoogle Scholar
12.Ghosh, A., Sharma, R. and Cho, J. T., Contact metric manifolds with η-parallel torsion tensor, Ann. Glob. Anal. Geom. 34 (2008), 287–299.Google Scholar
13.Gouli-Andreou, F. and Tsolakidou, N., Conformally flat contact metric manifolds with Q ξ = ρ ξ, Beitrage Alg. Geom. 45 (2004), 103–115.Google Scholar
14.Perelman, G., The entropy formula for the Ricci flow and its geometric applications submitted, 2002; accessed, 2003, available at: http://arXiv.org/abs/math.DG/02111159.Google Scholar
15.Sharma, R., Certain results on K-contact and (k, μ)-contact manifolds, J. Geom. 89 (2008), 138–147.CrossRefGoogle Scholar
16.Sharma, R. and Ghosh, A., Sasakian 3-metric as a Ricci soliton represents the Heisenberg group, Int. J. Geom. Methods Math.Phys. 8 (2011), 149–154.Google Scholar
17.Sharma, R. and Ghosh, A., A generalization of K-contact and (K, μ)-contact manifolds, submitted.Google Scholar
18.Tanno, S., Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad. 43 (1967), 581–583.Google Scholar