Ricci张量对称函数的预定问题  

The Prescribing Problem for Symmetric Function of Ricci Tensor

作　　者：贺妍 张维维 Yan HE;Wei Wei ZHANG(Hubei Key Laboratory of Applied Mathematics,Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,P.R.China;School of Finance,Chongqing Technology and Business University,Chongqing 400064,P.R.China)

机构地区：[1]湖北大学数学与统计学学院应用数学湖北省重点实验室,武汉430062 [2]重庆工商大学财政金融学院,重庆400064

出　　处：《数学学报（中文版）》2021年第1期41-46,共6页Acta Mathematica Sinica：Chinese Series

基　　金：应用数学湖北省重点实验室开放基金资助项目。

摘　　要：本文考虑Ricci张量的对称函数σ2 (Ricg)的预定问题.假设(M,g)是闭的Einstein流形,我们得到了只要流形(M,g)不具有σ2 (Ric)奇性,则对于变号的函数f∈C^∞(M),存在度量g^*,使得σ2 (Ricg^*)=f.然后,作为推论,得到了具有负数量曲率的闭Einstein流形上的预定曲率的结果.We consider the prescribing problem for symmetric function of Ricci tensor.Suppose a closed Einstein manifold(M,g) is not σ2(Ric) singular.Let f∈C^∞(M) and it changes sign.We prove that there exists a metric g^* such that σ2(Ricg^*)=f.Then,as a corollary,we have an existence result for the prescribing problem for Einstein manifold with negative scalar curvature.

关 键 词：对称函数 RICCI张量 预定曲率问题 

分 类 号：O186[理学—基础数学]