ON CONFORMALLY FLAT MANIFOLDS WITH CONSTANT POSITIVE SCALAR CURVATURE

被引：21

作者：

Catino, Giovanni ^{[1
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 06期

关键词：

Conformally flat manifold; rigidity; DEFORMATION;

D O I：

10.1090/proc/12925

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We classify compact conformally flat n-dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isometrically by either S-n with the round metric, S-1 x Sn-1 with the product metric or S-1 x Sn-1 with a rotationally symmetric Derdzinski metric.

引用

页码：2627 / 2634

页数：8

共 29 条

[1]

[Anonymous], 1952, Comment. Math. Helv, DOI [DOI 10.1007/BF02564308, 10.1007/BF02564308]

[2]

BERGER M, 1969, J DIFFER GEOM, V3, P379

[3] VECTOR FIELDS AND RICCI CURVATURE [J].

BOCHNER, S .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1946, 52 (09) :776-797

[4]

Bourguignon J.P., 1990, Progress in Nonlinear Differential Equations and Their Applications, V4, P251

[5] Conformally flat manifolds with nonnegative Ricci curvature [J].

Carron, G ;

Herzlich, M .

COMPOSITIO MATHEMATICA, 2006, 142 (03) :798-810

[6] A note on Codazzi tensors [J].

Catino, Giovanni ;

Mantegazza, Carlo ;

Mazzieri, Lorenzo .

MATHEMATISCHE ANNALEN, 2015, 362 (1-2) :629-638

[7] Compact locally conformally flat Riemannian manifolds [J].

Cheng, QM .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2001, 33 :459-465

[8] ON COMPACT RIEMANNIAN-MANIFOLDS WITH HARMONIC CURVATURE [J].

DERDZINSKI, A .

MATHEMATISCHE ANNALEN, 1982, 259 (02) :145-152

[9]

DeTurck D. M., 1989, Forum Math., V1, P377, DOI DOI 10.1515/FORM.1989.1.377

[10]

Goldberg S.I., 1969, KODAI MATH SEM REP, V21, P226, DOI DOI 10.2996/KMJ/1138845885

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