弱 Berwald 双挠积 Finsler 度量
Weakly Berwald Doubly-Twisted Product Finsler Metrics
DOI: 10.12677/PM.2021.117156, PDF, HTML,    国家自然科学基金支持
作者: 邓香香, 何 勇*, 倪琪慧：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: Finsler 度量；双挠积；弱 Berwald 度量；迷向平均 Berwald 曲率；Finsler Metrics； Doubly Twisted Product； Weakly Berwald Metrics； Isotropic Mean Berwald Curvature
摘要: 本文主要研究了双挠积 Finsler 度量的平均 Berwald 曲率和迷向平均 Berwald 曲率，给出了双 挠积 Finsler 度量是弱 Berwald 度量的充要条件，证明了在一定条件下具有迷向平均 Berwald 曲率的双挠积 Finsler 度量是弱 Berwald 度量。
Abstract: This paper mainly studies the mean Berwald curvature and isotropic mean Berwald curvature doubly-twisted product of Finsler metrics. The necessary and sufficient conditions for the doubly-twisted product of Finsler metrics are weakly Berwald metrics. It is proved that under certain conditions the doubly-twisted product of Finsler metrics with isotropic mean Berwald curvature is weakly Berwald metrics.
文章引用：邓香香, 何勇, 倪琪慧. 弱 Berwald 双挠积 Finsler 度量[J]. 理论数学, 2021, 11(7): 1389-1399. https://doi.org/10.12677/PM.2021.117156

参考文献

[1] Chen, B.Y. (1981) Geometry of Submanifolds and Its Applications. Science University of Toky- o, III, Tokyo.
[2] Kozma, L., Peter, I.R. and Shimada, H. (2006) On the Twisted Product of Finsler Manifolds. Reports on Mathematical Physics, 57, 375-383.
https://doi.org/10.1016/S0034-4877(06)80028-5
[3] Peyghan, E., Tayebi, A. and Far, L.N. (2013) On Twisted Products Finsler Manifolds. ISRN Geometry, 2013, Article ID: 732432.
https://doi.org/10.1155/2013/732432
[4] Nibaruta, G., Karimumuryango, M., Nibirantiza, A. and Ndayirukiye, D. (2020) Twisted Prod- ucts Berwald Metrics of Polar Type. Differential Geometry-Dynamical Systems, 22, 183-193.
[5] Berwald, L. (1926) Untersuchung der Kru¨mmung allgemeiner metrischer R¨aume auf Grund des in ihnen herrschenden Parallelismus. Mathematische Zeitschrift, 25, 40-73.
https://doi.org/10.1007/BF01283825
[6] Berwald, L. (1928) Parallelu´bertragung in allgemeinen R¨aumen. Atti Del Congresso Inter- nazionale Dei Matematici Bologna Del Al De Settembre Di, 4, 263-270.
[7] Matsumoto, M. (1986) Foundation of Finsler Geometry and Special Finsler Spaces. Kaiseisha Press, Otsu, Japan.
[8] Shen, Z. (2001) Differential Geometry of Spray and Finsler Spaces. Springer, The Netherlands.
[9] Chen, X. and Shen, Z. (2005) On Douglas Metrics. Publicationes Mathematicae, 66, 503-503.
[10] Yang, Z., He, Y. and Zhang, X. (2020) S-Curvature of Doubly Warped Product of Finsler Manifolds. Acta Mathematica Sinica, 36, 95-101.
[11] Bao, D., Chern, S.S. and Shen, Z. (2000) An Introduction to Riemann-Finsler Geometry. Springer-Verlag, New York.
[12] 沈一兵, 沈忠民. 现代芬斯勒几何初步[M]. 北京: 高等教育出版社, 2013.
[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.
https://doi.org/10.4064/ap105-3-6

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