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数学进展 - 2020, Vol. 49(4): 453-462
研究论文
广义${(\alpha,\beta)}$-度量的共形向量场
On Conformal Vector Fields of General ${(\alpha, \beta)}$-metrics

程新跃1, 徐穗云2
CHENG Xinyue1,*, XU Suiyun2

1.重庆师范大学数学科学学院, 重庆, 401331;
2.重庆理工大学理学院, 重庆, 400054
1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, P. R. China;
2. School of Sciences, Chongqing University of Technology, Chongqing, 400054, P. R. China

收稿日期: 2019-06-28
出版日期: 2020-08-11
2020, Vol. 49(4): 453-462
DOI: 10.11845/sxjz.2019072b


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摘要 本文主要研究了广义$(\alpha, \beta)$-度量的共形向量场. 我们在关于$\phi$的一定条件下刻画了广义$(\alpha, \beta)$-度量的共形向量场. 作为一个重要应用, 当$\alpha$ 具有常数截面曲率且$\beta$是关于$\alpha$的共形1-形式时, 我们完全决定了$(\alpha, \beta)$-度量的共形向量场.
关键词 广义$(\alpha,\beta)$-度量共形向量场共形1-形式截面曲率    
Abstract:In this paper, we mainly study conformal vector fields of general $(\alpha, \beta)$-metrics. We characterize the conformal vector fields of general $(\alpha, \beta)$-metrics with certain conditions about $\phi$. As a natural application, we completely determine conformal vector fields of $(\alpha, \beta)$-metrics when $\alpha$ has constant sectional curvature and $\beta$ is a conformal 1-form with respect to $\alpha$.
Key wordsgeneral $(\alpha,\beta)$-metric    conformal vector field    conformal 1-form    sectional curvature
PACS:  O186.14  
通讯作者: E-mail: * chengxy@cqnu.edu.cn   
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[2] 朱晴晴,杨标桂. 近凯勒流形中一般子流形的淹没[J]. 数学进展, 2016, 45(2): 271-289.
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