×

zbMATH — the first resource for mathematics

Ricci solitons on compact three-manifolds. (English) Zbl 0788.53034
In this short article we show that there are no compact three-dimensional Ricci solitons other than spaces of constant curvature. This generalizes a result obtained for surfaces by R. S. Hamilton [Contemp. Math. 71, 237-262 (1988; Zbl 0663.53031)]. The proof involves a careful analysis of the ODE for the curvature which is associated to the Ricci flow.
Reviewer: Th.Ivey (La Jolla)

MSC:
53C20 Global Riemannian geometry, including pinching
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chow, B., The Ricci flow on the 2-sphere, J. diff. geom., 33, 325-334, (1991) · Zbl 0734.53033
[2] Hamilton, R.S., Three manifolds with positive Ricci curvature, J. diff. geom., 17, 255-306, (1982) · Zbl 0504.53034
[3] Hamilton, R.S., Four manifolds with positive curvature operator, J. diff. geom., 24, 153-179, (1986) · Zbl 0628.53042
[4] Hamilton, R.S., The Ricci flow on surfaces, Contemporary mathematics, 71, 237-262, (1988)
[5] Margerin, C., Pointwise pinched manifolds are space forms, Proc. symp. pure math., 44, 307-328, (1986) · Zbl 0587.53042
[6] Mok, N., The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature, J. diff. geom., 27, 179-214, (1988) · Zbl 0642.53071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.