On gradient Ricci solitons conformal to a pseudo-Euclidean space

被引：24

作者：

Barbosa, Ezequiel ^{[1
]}

Pina, Romildo ^{[2
]}

Tenenblat, Keti ^{[3
]}

机构：

[1] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

[2] Univ Fed Goias, IME, BR-74001970 Goiania, Go, Brazil

[3] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2014年 / 200卷 / 01期

关键词：

Potential Function; Sectional Curvature; Einstein Manifold; Ricci Soliton; Riemannian Case;

D O I：

10.1007/s11856-014-0014-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider gradient Ricci solitons, conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n - 1)-dimensional translation group. We provide all such solutions in the case of steady gradient Ricci solitons.

引用

页码：213 / 224

页数：12

共 9 条

[1] Ricci solitons on Lorentzian manifolds with large isometry groups [J].

Batat, W. ;

Brozos-Vazquez, M. ;

Garcia-Rio, E. ;

Gavino-Fernandez, S. .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2011, 43 :1219-1227

[2]

Besse A.L., 1987, EINSTEIN MANIFOLDS

[3]

Brozos-Vasquez M., 2013, J GEOM ANAL, V13, P1196

[4] THREE-DIMENSIONAL LORENTZIAN HOMOGENEOUS RICCI SOLITONS [J].

Brozos-Vazquez, M. ;

Calvaruso, G. ;

Garcia-Rio, E. ;

Gavino-Fernandez, S. .

ISRAEL JOURNAL OF MATHEMATICS, 2012, 188 (01) :385-403

[5]

Bryant R, LOCAL EXISTENC UNPUB

[6] ON LOCALLY CONFORMALLY FLAT GRADIENT STEADY RICCI SOLITONS [J].

Cao, Huai-Dong ;

Chen, Qiang .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (05) :2377-2391

[7]

Davis H.T., 1962, Introduction to Nonlinear Differential and Integral Equations

[8] Rigidity of shrinking Ricci solitons [J].

Fernandez-Lopez, Manuel ;

Garcia-Rio, Eduardo .

MATHEMATISCHE ZEITSCHRIFT, 2011, 269 (1-2) :461-466

[9] Lorentz Ricci Solitons on 3-dimensional Lie groups [J].

Onda, Kensuke .

GEOMETRIAE DEDICATA, 2010, 147 (01) :313-322

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