A gap theorem for complete noncompact manifolds with nonnegative Ricci curvature

被引：17

作者：

Chen, BL ^{[1
]}

Zhu, XP ^{[1
]}

机构：

[1] Zhongshan Univ, Dept Math, Guangzhou 510275, Peoples R China

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2002年 / 10卷 / 01期

关键词：

D O I：

10.4310/CAG.2002.v10.n1.a9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we obtain a gap theorem for the Ricci curvature over complete noncompact locally conformally flat manifolds. We prove that if the Ricci curvature is nonnegative and decays faster than quadratic at infinity, then the manifold is flat.

引用

页码：217 / 239

页数：23

共 19 条

[1] ON A CONSTRUCTION OF COORDINATES AT INFINITY ON MANIFOLDS WITH FAST CURVATURE DECAY AND MAXIMAL VOLUME GROWTH [J].

BANDO, S ;

KASUE, A ;

NAKAJIMA, H .

INVENTIONES MATHEMATICAE, 1989, 97 (02) :313-349

[2]

CHOW B, 1992, COMMUN PUR APPL MATH, V14, P1003

[3] CONTINUITY OF WEAK SOLUTIONS TO A GENERAL POROUS-MEDIUM EQUATION [J].

DIBENEDETTO, E .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1983, 32 (01) :83-118

[4] ASYMPTOTICALLY FLAT MANIFOLDS OF NONNEGATIVE CURVATURE [J].

DREES, G .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 1994, 4 (01) :77-90

[5]

ESCHENBURG JH, 1989, J DIFFER GEOM, V30, P155

[6] GAP THEOREMS FOR NON-COMPACT RIEMANNIAN-MANIFOLDS [J].

GREENE, RE ;

WU, H .

DUKE MATHEMATICAL JOURNAL, 1982, 49 (03) :731-756

[7]

HAMILTON RS, 1993, J DIFFER GEOM, V37, P225

[8]

HAMILTON RS, 1986, J DIFFER GEOM, V24, P153

[9] A CERTAIN PROPERTY OF SOLUTIONS OF PARABOLIC EQUATIONS WITH MEASURABLE COEFFICIENTS [J].

KRYLOV, NV ;

SAFONOV, MV .

MATHEMATICS OF THE USSR-IZVESTIYA, 1981, 16 (01) :151-164

[10]

Ladyzhenskaya O., 1968, LINEAR QUASILINEAR E, DOI DOI 10.1090/MMONO/023

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