OALib Journal期刊
ISSN: 2333-9721
费用：99美元

投递稿件

查看量	下载量

相关文章
更多...

Pure Mathematics 2021

一类Finsler子流形的研究
The Study of a Class of Finsler Submanifolds

DOI: 10.12677/PM.2021.116116, PP. 1020-1030

晏文

Keywords: 自然恒等式，(α,β)-流形，极小子流形
A Natural Identity, (α,β)-Manifold, Minimal Submanifold

Full-Text Cite this paper Add to My Lib

Abstract:

本文主要利用一个自然恒等式并且考虑一类特殊(α,β)-流形 $\"\"$ 且φ(0)=1，其中？是Riemann度量， $\"\"$ 是一个1-形式。旨在利用自然恒等式研究一类特殊(α,β)-流形在一定条件下不存在闭的可定向的BH-极小子流形和闭的可定向的HT-极小曲面。
In this paper, we mainly use a natural identity and consider a class of special manifolds $\"\"$ with an？ (α,β)-metric $\"\"$ in which ？is the Riemannian metric, and $\"\"$ is a one-form. We aim to study a class of special manifolds by using the natural identity. Under certain conditions, there are no closed orientable BH-minimal submanifolds and closed orientable HT-minimal surfaces.

References

[1]	Matsumoto, M. (1992) Theory of Finsler Spaces with (α,β)-Metric. Reports on Mathematical Physics, 31, 43-83. https://doi.org/10.1016/0034-4877(92)90005-L
[2]	Antonelli, P.L., Ingarden, R.S. and Matsumoto, M. (1993) The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology. Kluwer Academic Publishers, Dordrecht. https://doi.org/10.1007/978-94-015-8194-3
[3]	Bejancu, A. (1990) Finsler Geometry and Applica-tions. Ellis Horwood Limited, Chichester.
[4]	Randers, G. (1941) On an Asymmetrical Metric in the Four-Space of General Relativity. Physical Review, 59, 285-290. https://doi.org/10.1103/PhysRev.59.195
[5]	Berwald, L. (1929) über Die N-Dimensionalen Geometrien Konstanter Krümmung, in Denen Die Geraden Die Kürzesten Sind. Mathematische Zeitschrift, 30, 449-469. https://doi.org/10.1007/BF01187782
[6]	Shen, Z. (1998) On Finsler Geometry of Submanifolds. Mathematische Annalen, 311, 549-576. https://doi.org/10.1007/s002080050200
[7]	Souza, M., Spruck, J. and Tenenblat, K. (2004) A Bernstein Type Theorem on a Randers Space. Mathematische Annalen, 329, 291-305. https://doi.org/10.1007/s00208-003-0500-3
[8]	He, Q. and Shen, Y.B. (2006) On the Mean Curvature of Finsler Submanifolds. Chinese Annals of Mathematics, 27, 663-674.
[9]	He, Q. and Shen, Y.B. (2006) On Bernstein Type Theorem in Finsler Geometry with Volume Form Induced from Sphere Bundle. Proceedings American Mathmatical So-ciety, 134, 871-880. https://doi.org/10.1090/S0002-9939-05-08017-2
[10]	Cui, N. and Shen, Y.B. (2009) Bern-stein Type Theorems for Minimal Surfaces in (α,β)-Space. Publicationes Mathematicae-Debrecen, 74, 383-400.
[11]	Cui, N. and Zhou, L.F. (2021) The Variation of a Functional on the Riemannian Submanifold and Its Applications. (Preprint)
[12]	Yu, C. and Zhu, H. (2011) On a New Class of Finsler Metrics. Differential Geometry and Its Applications, 29, 244-254. https://doi.org/10.1016/j.difgeo.2010.12.009
[13]	Yin, S., He, Q. and Xie, D. (2013) Minimal Submanifolds in General (α,β)-Spaces. Annales Polonici Mathematici, 108, 43-59. https://doi.org/10.4064/ap108-1-4
[14]	Cheng, X. and Shen, Z. (2009) A Class of Finsler Metrics with Isotropic S-Curvature. Israel Journal of Mathematics, 169, 317-340. https://doi.org/10.1007/s11856-009-0013-1
[15]	崔宁伟. 关于(α,β)-度量的S-曲率[J]. 数学物理学报, 2006, 26(6): 1047-1056.
[16]	Overath, P. (2014) Minimal Immersions in Finsler Spaces. PhD Thesis, RWTH Aachen University, Aachen.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

一类Finsler子流形的研究The Study of a Class of Finsler Submanifolds

一类Finsler子流形的研究
The Study of a Class of Finsler Submanifolds