On the non-negativity of the Ricci curvature on shrinking solitons

ZHANG Zhuhong

doi:10.13471/j.cnki.acta.snus.2018.06.020

您当前的位置：

首页 >

文章列表页 >

On the non-negativity of the Ricci curvature on shrinking solitons

更新时间：2023-12-11

- On the non-negativity of the Ricci curvature on shrinking solitons
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 6, Pages: 151-153(2018)
- 作者机构：
  
  华南师范大学数学科学学院,广东,广州,510631
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2018.06.020
  CLC：
- Published：2018，
  
  Published Online：25 November 2018，
扫描看全文
ZHANG Zhuhong. On the non-negativity of the Ricci curvature on shrinking solitons. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):151-153(2018)
DOI：

ZHANG Zhuhong. On the non-negativity of the Ricci curvature on shrinking solitons. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):151-153(2018) DOI： 10.13471/j.cnki.acta.snus.2018.06.020.

摘要

曲率的非负性是刻画流形的一个关键条件。证明了具有拼挤Weyl曲率的闭shrinking solitons上Ricci曲率一定是非负的。如果进一步假设Ricci曲率是正的，那么soliton是平凡的，即是Einstein流形。

Abstract

The non-negativity of curved is a key condition to characterize Riemannian manifolds. It is shown that any closed shrinking solitons with pinched Weyl curvature must have non-negative Ricci curvature. If further assume the soliton has positive Ricci curvature

then it must be trivial

that is

the solition is an Einstein manifold.

关键词

拼挤 Weyl 曲率shrinking soliton非负Ricci曲率极值原理

Keywords

pinched Weyl curvatureshrinking solitonnon-negative Ricci curvaturemaximum principle

references

Views

154

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Postal code：510275
Tel：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09064830号-19 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰