全部 标题 作者
关键词 摘要

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...

两类Ricci二次闵可夫斯基积芬斯勒流形
Two Classes of Ricci Quadratic Minkowskian Product FinslerManifolds

DOI: 10.12677/PM.2026.162049, PP. 200-207

Keywords: 芬斯勒流形，闵可夫斯基积，Ricci二次，强 Ricci二次
Finsler Manifold, Minkowskian Product, Ricci Quadratic Form, Strongly Ricci Quadratic Form

Full-Text   Cite this paper   Add to My Lib

Abstract:

设(M1,F1)和(M2,F2)是两个芬斯勒流形,闵可夫斯基积芬斯勒流形(M,F)是赋予了芬斯勒度量F=√f(S,T)的乘积流形M= M1× M2,其中S= F12,T=F22,f是积函数.本文主要研究闵可夫斯基积芬斯勒流形的 Ricci 二次曲率,证明了闵可夫斯基积芬斯勒流形(M,F)是 Ricci二次流形当且仅当(M1,F1)和(M2,F2)都是 Ricci 二次流形;闵可夫斯基积芬斯勒流形(M,F)是强Ricci二次流形当且仅当(M1,F1)和(M2,F2)都是强 Ricci二次流形。
Let (M1,F1) and (M2,F2) be two Finsler manifolds. The Minkowskian product Finsler manifold (M,F) is the product manifold M= M1× M2 endowed with the Finsler metric F=√f(S,T), where S= F12,T=F22, and f denotes a product function. This paper mainly investigates the Ricci quadratic curvature of Minkowskian product Finsler manifolds, and proves the following results: The Minkowskian product Finsler man- ifold (M,F) is a Ricci quadratic manifold if and only if both (M1,F1) and (M2,F2) are Ricci quadratic manifolds; The Minkowskian product Finsler manifold (M,F) is a strongly Ricci quadratic manifold if and only if both (M1,F1) and (M2,F2) are strongly Ricci quadratic manifolds.

 References

[1]  Bacso, S. and Matsumoto, M. (1999) Finsler Spaces with the h-Curvature Tensor Dependent on Position Alone. Publicationes Mathematicae Debrecen, 55, 199-210.
https://doi.org/10.5486/pmd.1999.2274
[2]  Li, B. and Shen, Z. (2009) On Randers Metrics of Quadratic Riemann Curvature. International Journal of Mathematics, 20, 369-376.
https://doi.org/10.1142/s0129167x09005315
[3]  Sevim, E.S., Shen, Z. and  Ulgen, S. (2023) On Strongly Ricci-Quadratic Finsler Metrics. The Journal of Geometric Analysis, 33, Article No. 326.
https://doi.org/10.1007/s12220-023-01389-5
[4]  Sadeghzadeh, N. (2018) On Finsler Metrics of Quadratic Curvature. Journal of Geometry and Physics, 132, 75-83.
https://doi.org/10.1016/j.geomphys.2018.05.012
[5]  Mo, X. and Yu, Y. (2024) On Ricci-Quadratic Sprays (or Finsler) Spaces. Mediterranean Journal of Mathematics, 21, Article No. 211.
https://doi.org/10.1007/s00009-024-02742-w
[6]  Gabrani, M., Sevim, E.S. and  Ulgen, S. (2024) On a Class of Ricci Quadratic Finsler Metrics. Frontiers of Mathematics, 19, 851-864.
https://doi.org/10.1007/s11464-023-0046-5
[7]  Okada, T. (1982) Minkowskian Product of Finsler Spaces and Berwald Connection. Kyoto Journal of Mathematics, 22, 323-332.
https://doi.org/10.1215/kjm/1250521819
[8]  He, Y., Li, J., Bian, L. and Zhang, N. (2023) On Minkowskian Product of Finsler Manifolds. Differential Geometry and its Applications, 89, Article 102019.
https://doi.org/10.1016/j.difgeo.2023.102019
[9]  田畅，何勇,李淑雯,张辉.具有标量旗曲率的闵可夫斯基积芬斯勒度量[J].新疆师范大学学报(自然科学版)，2022,41(3): 55-63.
[10]  张娜,卢维娜,韩江慧,加依达尔·里扎别克.闵可夫斯基积芬斯勒度量的道格拉斯曲率和外尔曲率[J].新疆师范大学学报(自然科学版)，2023,42(1):67-74.
[11]  Bao, D., Chern, S.S. and Shen, Z.M. (2000) An Introduction to Riemann-Finsler Geometry. Springer Science.
[12]  Shen, Z.M. (2001) Differential Geometry of Spray and Finsler Spaces. Kluwer Academic Publishers.
[13]  栗嘉慧.Finsler度量的Minkowskian积[D]:[硕士学位论文].乌鲁木齐:新疆师范大学,2022.
[14]  Tian, C., He, Y., Lu, W. and Eryzabk, J. (2024) On Some Non-Riemannian Curvature of Minkowskian Product Finsler Metrics. Journal of Mathematical Analysis and Applications, 534, Article 128070.
https://doi.org/10.1016/j.jmaa.2023.128070

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133