具有势函数的拟-<i>F</i>-调和映射的若干结果

韩英波; 蒋凯歌; 张倩玉

doi:10.3969/j.issn.1003-0972.2018.01.002

具有势函数的拟-F-调和映射的若干结果

信阳师范学院数学与统计学院, 河南信阳 464000

基金项目:

国家自然科学基金项目（11201400）；信阳师范学院"南湖学者奖励计划"青年项目；河南省高校骨干教师培养计划项目（2016GGJS-096）；信阳师范学院研究生科研创新基金项目（2016KYJJ30）

详细信息

作者简介:
韩英波(1978-),男,山东菏泽人,副教授,博士,主要从事微分几何的研究.

中图分类号: O186.1
计量
- 文章访问数: 1116
- HTML全文浏览量: 65
- PDF下载量: 27
出版历程
- 收稿日期: 2017-01-11
- 修回日期: 2017-07-19
- 发布日期: 2018-01-09

Some Results for Quasi-F-harmonic Maps with Potential

College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

摘要

摘要: 引入了从光滑度量测度空间（M，g，e^-φ（x）dv_g）到黎曼流形中具有势函数的（弱）拟-F-调和映射的概念.在H和Bakry-Émery Ricci张量的条件下，利用应力-能量张量证明了上述映射的刘维尔型定理.
- 具有势函数的(弱)拟-F-调和映射 /
- 刘维尔型定理 /
- 应力-能量张量
Abstract: The notion of (weakly) quasi-F-harmonic map with potential was introduced from a smooth metric measure space (M,g,e^-φ(x)dv_g) into a Riemannian manifold. By using the stress-energy tensor, some Liouville type results were obtained for these maps under conditions on H and the Bakry-Émery Ricci tensor.
- (Weakly) Quasi-F-harmonic map with potential /
- Liouville type theorem /
- stress-energy tensor

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参考文献(11)

[1]	WANG Guofang, XU Deliang. Harmonic maps from smooth metric measure spaces[J]. International Journal of Mathematics, 2012, 23(9):1-21.
[2]	韩英波,张倩玉,喻丽菊.CC-稳态映射的刘维尔型定理[J].信阳师范学院学报(自然科学版),2017,30(1):22-27. HAN Yingbo, ZHANG Qianyu, YU Liju. Liouville type theorems for CC-stationary maps[J]. Journal of Xinyang Normal University (Natural Science Edition), 2017, 30(1):22-27.
[3]	FARDOUN A, RATTO A. Harmonic maps with potential[J]. Calculus of Variations and Partial Differential Equations, 1997, 5(2):183-197.
[4]	FENG Shuxiang, HAN Yingbo. Liouville type theorems of F-Harmonic maps with potential[J]. Results in Mathematics, 2014, 66(1/2):43-64.
[5]	HAN Yingbo, FENG Shuxiang. Monotonicity formulas and the stability of F-stationary maps with potential[J]. Houston Journal of Mathematics, 2014, 40(3):681-713.
[6]	韩英波,方联银,李静.带位势的弱F-调和映照的单调公式[J].信阳师范学院学报(自然科学版),2016,29(2):165-170. HAN Yingbo, FANG Lianyin, LI Jing. Monotonicity formulas of weakly F-Harmonic map with potential[J]. Journal of Xinyang Normal University (Natural Science Edition), 2016, 29(2):165-170.
[7]	XIN Y L. Geometry of harmonic maps[M]. Springer:Progress in Nonlinear Differential Equations and their Applications, 1996:23.
[8]	ARA M. Geometry of F-harmonic maps[J]. Kodai Mathematical Journal, 1999, 22(22):243-263.
[9]	DONG Yuxin, WEI S W. On vanishing theorems for vector bundle valued p-Forms and their applications[J]. Communications in Mathematical Physics, 2011, 304(2):329-368.
[10]	DONG Yuxin, LIN Hezi, YANG Guilin. Liouville theorems for F-Harmonic maps and their applications[J]. Results in Mathematics, 2016, 69(1/2):105-127.
[11]	HAN Y B, LI Y, REN Y B, et al. New comparison theorems in Riemannian geometry[J]. Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 2014, 9(2):163-186.

施引文献(4)

期刊类型引用(4)

1.	种田，邱紫阳. F-H-调和映照的刘维尔型定理. 华中师范大学学报(自然科学版). 2024(05): 519-525 . 百度学术
2.	韩英波，王艳，薛玉莹. F-稳态映射的刘维尔型定理. 信阳师范学院学报(自然科学版). 2021(01): 16-21 . 本站查看
3.	冯书香，蒋凯歌，李静. F-CC调和映射的若干结果. 信阳师范学院学报(自然科学版). 2020(01): 31-36 . 本站查看
4.	韩英波，蒋凯歌，张倩玉. Hadamard流形中子流形的p-调和函数的刘维尔型定理. 信阳师范学院学报(自然科学版). 2019(01): 11-16 . 本站查看