弱Landsberg共形双扭曲积芬斯勒度量

doi:10.12677/pm.2025.1512304

期刊菜单

弱Landsberg共形双扭曲积芬斯勒度量
Weak Landsberg Conformally Doubly Warped Product Finsler Metrics

DOI: 10.12677/pm.2025.1512304, PDF, 国家自然科学基金支持
作者: 杨蕊嘉, 何勇^*, 侯传燕, 陈静雅：新疆师范大学数学科学学院，新疆乌鲁木齐
关键词: 芬斯勒度量；共形双扭曲积；弱Landsberg度量；相对迷向平均Landsberg曲率；Finsler Metric； Conformally Doubly Warped Product； Weak Landsberg Metric； Relatively Isotropic Mean Landsberg Curvature

摘要: 本文证明了两个非黎曼的芬斯勒度量

F_{1}

和

F_{2}

的共形双扭曲积

F

是弱Landsberg度量当且仅当

F_{1}

和

F_{2}

均为弱Landsberg度量且

F

为乘积芬斯勒度量，并证明了若

F

具有相对迷向平均Landsberg曲率，则其为弱Landsberg度量。

Abstract: We prove that a Conformally Doubly Warped Product

F

of two non-Riemannian Finsler metrics

F_{1}

and

F_{2}

is a weak Landsberg metric if and only if both

F_{1}

and

F_{2}

are weak Landsberg metrics and

F

is a product Finsler metric. Furthermore, we prove that if

F

has relatively isotropic mean Landsberg curvature, then it is a weak Landsberg metric.

文章引用：杨蕊嘉, 何勇, 侯传燕, 陈静雅. 弱Landsberg共形双扭曲积芬斯勒度量[J]. 理论数学, 2025, 15(12): 154-164. https://doi.org/10.12677/pm.2025.1512304

参考文献

[1]	Berwald, L. (1928) Parallelubertagung in Allgemeinen Raumen. Atti del Congresso Internazionale dei Matematici, 4, 263-270.
[2]	Shen, Z.M. (2001) Differential Geometry of Spray and Finsler Spaces. Kluwer Academic Publishers.
[3]	Shen, Z.M. (2004) Landsberg Curvature, S-Curvature and Riemann Curvature. In: Bao, D., Bryant, R.L., Chern, S.S. and Shen, Z., Eds., A Sampler of Riemann-Finsler Geometry, Cambridge University Press, 303-356.
[4]	Li, B. and Shen, Z. (2007) On a Class of Weak Landsberg Metrics. Science in China Series A: Mathematics, 50, 573-589. [Google Scholar] [CrossRef]
[5]	Najafi, B. and Tayebi, A. (2017) Weakly Stretch Finsler Metrics. Publicationes Mathematicae Debrecen, 91, 441-454. [Google Scholar] [CrossRef]
[6]	Tayebi, A. and Najafi, B. (2024) Conformally Closed Weakly Landsberg Metrics. Acta Mathematica Universitatis Comenianae, 93, 71-78.
[7]	Chen, X. and Shen, Z. (2005) On Douglas Metrics. Publicationes Mathematicae Debrecen, 66, 503-512. [Google Scholar] [CrossRef]
[8]	Cheng, X., Wang, H. and Wang, M. (2008)-Metrics with Relatively Isotropic Mean Landsberg Curvature. Publicationes Mathematicae Debrecen, 72, 475-485. [Google Scholar] [CrossRef]
[9]	Cheng, X., Li, H. and Zou, Y. (2014) On Conformally Flat-Metrics with Relatively Isotropic Mean Landsberg Curvature. Publicationes Mathematicae Debrecen, 85, 131-144. [Google Scholar] [CrossRef]
[10]	Soleiman, A. and Abdelsalam, A.M. (2019) On Conformally Doubly Warped Product Finsler Manifold. Journal of the Egyptian Mathematical Society, 27, Article No. 55. [Google Scholar] [CrossRef]
[11]	加依达尔·里扎别克, 何勇, 杨蕊嘉, 等. 弱贝瓦尔德共形双扭曲积芬斯勒度量[J]. 淮阴师范学院学报(自然科学版), 2025, 24(3): 189-197+, 212.
[12]	杨蕊嘉, 何勇. 共形双扭曲积芬斯勒度量的局部对偶平坦性[J/OL]. 新疆师范大学学报(自然科学版), 1-6. 2025-12-17. [Google Scholar] [CrossRef]
[13]	Peyghan, E., Tayebi, A. and Najafi, B. (2012) Doubly Warped Product Finsler Manifolds with Some Non-Riemannian Curvature Properties. Annales Polonici Mathematici, 105, 293-311. [Google Scholar] [CrossRef]
[14]	加依达尔∙里扎别克. 关于共形双扭曲积芬斯勒度量的几类性质研究[D]: [硕士学位论文]. 乌鲁木齐: 新疆师范大学, 2025.
[15]	Bao, D., Chern, S.S. and Shen, Z.M. (2000) An Introduction to Riemann-Finsler Geometry. Springer.
[16]	Bian, L.Z., He, Y. and Han, J.H. (2023) Landsberg Curvature of Twisted Product Finsler Metric. arXiv: 2305.05468.

为你推荐

友情链接