Abstract
In this paper, we give some fundamental equations of curvature tensors on Berwald submersions, which imply the relationship of flag curvatures of the associated manifolds and the fibers.
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References
M. Abate, G. Patrizio, Finsler Metric—A Global Approach, vol. 1591, Lecture Notes in Math (Springer, Berlin, 1994)
W. Ambrose, I.M. Singer, On homogeneous Riemannian manifolds. Duke Math. J. 25, 647–669 (1958)
W. Chen, X. Li, An Introduction to Riemann Ieometry (Peking University Press, Beijing, 2004). (in Chinese)
S.S. Chern, Z. Shen, Riemann–Finsler Geometry (World Scientific, Singapore, 2005)
S. Deng, Z. Hou, Invariant Finsler metrics on homogeneous manifolds. J. Phys. A Math. Gen. 37, 8245–8253 (2004)
S. Deng, Z. Hou, On symmetric Finsler spaces. Isr. J. Math. 162, 197–219 (2007)
S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, 2nd edn. (Academic Press, London, 1978)
S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. I (Interscience, New York, II, 1963)
B. O’Neill, The fundamental equations of a submersion. Mich. Math. J. 13, 459–469 (1966)
Z. Szabó, Positive definite Berwald spaces (Structure Theorems on Berwald spaces). Tensor, N. S. 35, 25–39 (1981)
R. Yan, Affinely equivalent K\(\ddot{a}\)hler-Finsler metrics on a complex manifold. Sci. China Math. 55, 731–738 (2012)
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Supported by the National Natural Science Foundation of China (11571287,11871405) and the Natural Science Foundation of Fujian Province of China (2016J01034).
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Yan, R. Flag curvatures on Berwald submersions. Period Math Hung 81, 115–122 (2020). https://doi.org/10.1007/s10998-020-00319-0
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DOI: https://doi.org/10.1007/s10998-020-00319-0