旋转对称梯度山叶孤子

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-08-06 DOI:10.1007/s00013-024-02032-7

Antonio W. Cunha, Rong Mi

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引用次数: 0

摘要

这篇短文论述了具有恒定标量曲率度量的紧凑、完整和非紧凑梯度山边孤子（M, g, f）。首先，我们给出了梯度紧凑山边孤子的新的三性证明。此外，在一些积分条件下，我们还能改进 Ma 和 Miquel 的一个结果（Ann Global Anal Geom 42:195-205, 2012）。最后，我们得到山边公设变得旋转对称了。这里还得到了 k-Yamabe 孤子的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Rotationally symmetric gradient Yamabe solitons

This short note deals with compact and complete and non-compact gradient Yamabe solitons (M, g, f) such that it has metric of constant scalar curvature. Firstly, we give a new proof of triviality for gradient compact Yamabe solitons. Also, under some integral conditions, we are able to improve a result due to Ma and Miquel (Ann Global Anal Geom 42:195–205, 2012). Finally, we obtain that the Yamabe metric becomes rotationally symmetric. Results for k-Yamabe solitons are also obtained here.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.