关于标量曲率与简明场方程的注记

IF 0.4 Q4 MATHEMATICS

International Electronic Journal of Geometry Pub Date : 2021-03-30 DOI:10.36890/IEJG.906792

Ramesh Sharma, Sharief Deshmukh

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引用次数: 0

摘要

我们证明了黎曼流形M的标量曲率是常数，如果它满足（i）闭域方程，并且M是紧致的，（ii）特殊闭域方程。最后，我们证明了，如果一个完全连通的黎曼流形允许一个保持标量曲率不变的稠非等距向量场，并且保角函数是特殊的稠函数，那么标量曲率是一个常数。

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Remarks on Scalar Curvature and Concircular Field Equation

We show that the scalar curvature of a Riemannian manifold M is constant if it satisﬁes (i) the concircular ﬁeld equation and M is compact, (ii) the special concircular ﬁeld equation. Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector ﬁeld leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.

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来源期刊

International Electronic Journal of Geometry MATHEMATICS-

CiteScore

0.80

自引率

14.30%

发文量