Hostname: page-component-6bf8c574d5-w79xw Total loading time: 0 Render date: 2025-02-23T02:00:04.976Z Has data issue: false hasContentIssue false
  • English
  • Français

INTEGRAL FORMULAE ON QUASI-EINSTEIN MANIFOLDS AND APPLICATIONS

Published online by Cambridge University Press:  09 December 2011

A. BARROS  and
E. RIBEIRO JR.
A. BARROS
Affiliation:
Departamento de Matemática-Universidade Federal do Ceará, 60455-760-Fortaleza-CE, Brazil e-mail: [email protected], [email protected]
E. RIBEIRO JR.
Affiliation:
Departamento de Matemática-Universidade Federal do Ceará, 60455-760-Fortaleza-CE, Brazil e-mail: [email protected], [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.

The aim of this paper is to extend for the m-quasi-Einstein metrics some integral formulae obtained in [1] (C. Aquino, A. Barros and E. Ribeiro Jr., Some applications of the Hodge-de Rham decomposition to Ricci solitons, Results Math. 60 (2011), 245–254) for Ricci solitons and derive similar results achieved there. Moreover, we shall extend the m-Bakry-Emery Ricci tensor for a vector field X on a Riemannian manifold instead of a gradient field ∇f, in order to obtain some results concerning these manifolds that generalize their correspondents to a gradient field.

Keywords

Primary 53C2553C2053C21secondary 53C65
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 213 - 223
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Aquino, C., Barros, A. and Ribeiro, E. Jr, Some applications of the Hodge-de Rham decomposition to Ricci solitons, Results Math. 60 (2011), 245–254. Doi:10.1007/s00025-01100166-1.CrossRefGoogle Scholar
2.Bourguignon, J. P. and Ezin, J. P., Scalar curvature functions in a conformal class of metrics and conformal transformations, Trans. Am. Math. Soc. 301 (1987), 723–736.CrossRefGoogle Scholar
3.Camargo, F., Caminha, A. and Souza, P., Complete foliations of space forms by hypersurfaces, Bull. Braz. Math. Soc. 41 (2010), 339–353.Google Scholar
4.Case, J., On the nonexistence of quasi-Einstein metrics, Pacific J. Math. 248 (2010), 227–284.CrossRefGoogle Scholar
5.Case, J., Shu, Y. and Wei, G., Rigity of quasi-Einstein metrics, Diff. Geo. Appl. 29 (2010), 93–100.CrossRefGoogle Scholar
6.Eminenti, M., La Nave, G. and Mantegazza, C., Ricci solitons: The equation point of view, Manuscripta Math. 127 (2008), 345–367.CrossRefGoogle Scholar
7.Hamilton, R. S., The formation of singularities in the Ricci flow, Surv. Diff. Geom. 2 (1993), 7–136 (International Press, Cambridge, MA).CrossRefGoogle Scholar
8.Ishihara, S. and Tashiro, Y., On Riemannian manifolds admitting a concircular transformation, Math. J. Okayama Univ. 9 (1959), 19–47.Google Scholar
9.Kim, D. S. and Kim, Y. H., Compact Einstein warped product spaces with nonpositive scalar curvature, Proc. Am. Math. Soc. 131 (2003), 2573–2576.CrossRefGoogle Scholar
10.Petersen, P. and Wylie, W., Rigidity of gradient Ricci solitons, Pacific J. Math. 241 (2009), 329–345.CrossRefGoogle Scholar
11.Yau, S. T., Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659–670.CrossRefGoogle Scholar