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理论数学
Vol. 12 No. 10 (October 2022)
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双曲 Kenmotsu 流形上的近 Yamabe孤立子
Almost Yamabe Solitons on Hyperbolic Kenmotsu Manifolds
DOI:
10.12677/PM.2022.1210178
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被引量
下载: 243
浏览: 383
国家自然科学基金支持
作者:
韩和龙
*
,
刘建成
#
:西北师范大学数学与统计学院,甘肃 兰州
关键词:
双曲 Kenmotsu 流形
;
共形向量场
;
近 Yamabe 孤立子
;
Killing 向量场
;
Hyperbolic Kenmotsu Manifold
;
Conformal Vector Field
;
Almost Yamabe Soliton
;
Killing Vector Field
摘要:
利用 Lie 导数算子,协变微分算子以及共形向量场的性质,证明在具有双曲 Kenmotsu 结构的近 Yamabe 孤立子中, 如果存在光滑函数f,使得切触1−形式η不变,则其势向量场是 Killing 向量场。
Abstract:
By using the properties of Lie-derivative operator, covariant derivative operator and conformal vector field, we prove that in almost Yamabe solitons with hyperbolic Kenmotsu structrue, if there exists a smooth function f that leaves the contact 1-form η invariant, then its potential vector fields are Killing vector fields.
文章引用:
韩和龙, 刘建成. 双曲 Kenmotsu 流形上的近 Yamabe孤立子[J]. 理论数学, 2022, 12(10): 1649-1654.
https://doi.org/10.12677/PM.2022.1210178
参考文献
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[3]
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[4]
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[6]
Barbosa, E. and Ribeiro, E. (2013) On Conformal Solutions of the Yamabe Flow. Archiv der Mathematik, 101, 79-89.
https://doi.org/10.1007/s00013-013-0533-0
[7]
Upadhyay, M.D. and Dube, K.K. (1976) Almost Contact Hyperbolic (f, g, η, ξ)-Structure. Acta Mathematica Academiae Scientiarum Hungarica, 28, 13-15.
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Kenmotsu, K. (1972) A Class of Almost Contact Riemannian Manifolds. Tohoku Mathematical Journal, 24, 93-103.
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[9]
Ghosh, A. (2021) Ricci Almost Soliton and Almost Yamabe Soliton on Kenmotsu Manifold. Asian-European Journal of Mathematics, 14, 4-20.
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[10]
Pankaj, S.K. and Chaubey, G.A. (2021) Yamabe and Gradient Yamabe Solitons on 3- Dimensional Hyperbolic Kenmotsu Manifolds. Differential Geometry-Dynamical Systems, 23, 176-184.
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