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Rigid Properties of Quasi-almost-Einstein Metrics

Rigid Properties of Quasi-almost-Einstein Metrics
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摘要 In this paper,quasi-almost-Einstein metrics on complete manifolds are studied.Two examples are given and several formulas are established.With the help of these formulas,the author proves rigid results on compact or noncompact manifolds,in which some basic tools,such as the weighted volume comparison theorem and the weak maximum principle at infinity,are used.A lower bound estimate for the scalar curvature is also obtained.
作者 Linfeng WANG
机构地区 School of Science
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第5期715-736,共22页 数学年刊（B辑英文版）
基金 Project supported by the National Natural Science Foundation of China(Nos.10971066,11171254)
关键词 Quasi-almost-Einstein metric Potential function Gradient estimate Rigid property 爱因斯坦 刚性 度量 属性 体积比较定理 弱极值原理 完备流形 非紧流形
分类号 O412.1 [理学—理论物理] TQ325.14 [化学工程—合成树脂塑料工业]
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  • 1Hamilton, R.: Three-manifolds with positive Ricci curvature. J. Differential Geom., 17(2), 255-306 (1982).
  • 2Munteanu, O.: The volume growth of complete gradient Shrinking Ricci solitons, axxiv:math.DG/0904.0798.
  • 3Cao, H. D., Zhou, D.: On complete gradient shrinking solitons. J. Differential Geom., 85, 175-186 (2010).
  • 4Carrillo, J., Ni, L.: Sharp logarithmic sobolev inequalities on gradient solitons and applications. Comm. Anal. Geom., 17, 721-753 (2009).
  • 5Zhang, Z. H.: On the completeness of gradient Ricci solitons. Proc. Amer. Math. Sot., 137, 2755-2759 (2009).
  • 6Chen, B. L.: Strong uniqueness of the Ricci flow. J. Differential Geom., 82, 363-382 (2009).
  • 7Chow, B., Lu, P., Ni, L.: Hamilton's Ricci Flow, Amer. Math. Soc., Providence, RI, 2006.
  • 8Gao, H. D.: Geometry of Ricci solitons. Chin. Ann. Math. Set. B, 27(2), 121-142 (2006).
  • 9Pigola, S., Rimoldi, M., Setti, A.: Remarks on non-compact gradient Ricci solitons, arxiv: math,DG/ 0905.2868v3.
  • 10Fang, F. Q., Man, J. W., Zhang, Z. L.: Complete gradient shrinking Pdcci solitons have finite topological type. C. R. Acad. Sci. Paris, 346, 653-656 (2008).

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Chinese Annals of Mathematics,Series B
2012年 第5期

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