Gradient Ricci solitons admitting a closed conformal Vector field

被引：9

作者：

Diogenes, R. ^{[1
]}

Ribeiro, E., Jr. ^{[2
]}

Silva Filho, J. ^{[1
]}

机构：

[1] Univ Integracao Int Lusofonia Afro Brasileira UNI, Inst Ciencias Exatas & Nat, BR-62785000 Acarape, CE, Brazil

[2] Univ Fed Ceara, Dept Matemat, Campus Pici,Ave Humberto Monte,Bloco 914, BR-60455760 Fortaleza, CE, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 455卷 / 02期

关键词：

Ricci soliton; Ricci flow; Conformal vector field; RIEMANNIAN SPACES;

D O I：

10.1016/j.jmaa.2017.06.071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a gradient Ricci soliton (M-n, g) admitting a nonparallel closed conformal vector field must be locally conformally flat, provided that the dimension is 3 or 4. Moreover, in the dimension n >= 5, we show that a gradient Ricci soliton admitting a nonparallel closed conformal vector field must have harmonic Weyl tensor. In particular, we conclude that a gradient shrinking Ricci soliton admitting a nonparallel closed conformal vector field must be rigid. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1975 / 1983

页数：9

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