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, PDF, HTML,    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

[1] Cao, H.D., Sun, X. and Zhang, Y. (2012) On the Structure of Gradient Yamabe Solitons. Mathematical Research Letters, 19, 767-774. [Google Scholar] [CrossRef] 
[2] Daskalopoulos, P. and Sesum, N. (2013) The Classification of Locally Conformally Flat Yamabe Solitons. Advances in Mathematics, 240, 346-369.[CrossRef] 
[3] Chen, B.Y. and Deshmukh, S. (2018) Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds. Mediterranean Journal of Mathematics, 15, Article No. 194. [Google Scholar] [CrossRef] 
[4] Ma, L. and Cheng, L. (2011) Properties of Complete Non-Compact Yamabe Solitons. Annals of Global Analysis and Geometry, 40, 379-387. [Google Scholar] [CrossRef] 
[5] Hsu, S.Y. (2018) A Note on Compact Gradient Yamabe Solitons. Mathematical Analysis and Applications, 388, 725-726. [Google Scholar] [CrossRef] 
[6] Barbosa, E. and Ribeiro, E. (2013) On Conformal Solutions of the Yamabe Flow. Archiv der Mathematik, 101, 79-89. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[8] Kenmotsu, K. (1972) A Class of Almost Contact Riemannian Manifolds. Tohoku Mathematical Journal, 24, 93-103. [Google Scholar] [CrossRef] 
[9] Ghosh, A. (2021) Ricci Almost Soliton and Almost Yamabe Soliton on Kenmotsu Manifold. Asian-European Journal of Mathematics, 14, 4-20. [Google Scholar] [CrossRef] 
[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.
[11] Yano, K. (1970) Integral Formulas in Riemannian Geometry. Marcel Dekker, New York.

为你推荐