Some fundamental problems in global Finsler geometry

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Cheng Xinyue

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Journal Paper

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Journal: AUT Journal of Mathematics and Computing Year:2021 | Volume:2 | Issue:2 Page(s): 185-198

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Information Journal Paper

Title

Some fundamental problems in global Finsler geometry

Author(s)

Cheng Xinyue | Issue Writer Certificate

Keywords

Dual Finsler metric

Gradient vector

eld

Finsler Laplacian

Eigenvalue

Hessian

Lie derivative

Weighted Ricci curvature

Abstract

The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this survey article, we introduce some important and fundamental topics in global Finsler geometry and discuss the related properties and the relationships in them. In particular, we optimize and improve the various de, nitions of Lie derivatives on Finsler manifolds. Further, we also obtain an estimate of lower bound for the non-zero Eigenvalues of the Finsler Laplacian under the condition that RicN ,K > 0.

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APA: Copy

Cheng, Xinyue. (2021). Some fundamental problems in global Finsler geometry. AUT JOURNAL OF MATHEMATICS AND COMPUTING, 2(2), 185-198. SID. https://sid.ir/paper/1043874/en

Vancouver: Copy

Cheng Xinyue. Some fundamental problems in global Finsler geometry. AUT JOURNAL OF MATHEMATICS AND COMPUTING[Internet]. 2021;2(2):185-198. Available from: https://sid.ir/paper/1043874/en

IEEE: Copy

Xinyue Cheng, “Some fundamental problems in global Finsler geometry,” AUT JOURNAL OF MATHEMATICS AND COMPUTING, vol. 2, no. 2, pp. 185–198, 2021, [Online]. Available: https://sid.ir/paper/1043874/en

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