Ricci张量对称函数的预定问题
The Prescribing Problem for Symmetric Function of Ricci Tensor
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.
对称函数 / Ricci张量 / 预定曲率问题 {{custom_keyword}} /
symmetric function / Prescribing problem / ricci tensor {{custom_keyword}} /
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