Ricci张量对称函数的预定问题

贺妍, 张维维

数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 41-46.

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PDF(385 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 41-46. DOI: 10.12386/A2021sxxb0002
论文

Ricci张量对称函数的预定问题

    贺妍1, 张维维2
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The Prescribing Problem for Symmetric Function of Ricci Tensor

    Yan HE1, Wei Wei ZHANG2
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文章历史 +

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fCM),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.

Abstract

We consider the prescribing problem for symmetric function of Ricci tensor. Suppose a closed Einstein manifold (M, g) is not σ2(Ric) singular. Let fC(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

Key words

symmetric function / Prescribing problem / ricci tensor

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贺妍, 张维维. Ricci张量对称函数的预定问题. 数学学报, 2021, 64(1): 41-46 https://doi.org/10.12386/A2021sxxb0002
Yan HE, Wei Wei ZHANG. The Prescribing Problem for Symmetric Function of Ricci Tensor. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 41-46 https://doi.org/10.12386/A2021sxxb0002

参考文献

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基金

应用数学湖北省重点实验室开放基金资助项目

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