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Some fundamental problems in global Finsler geometry | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 2، شماره 2، آذر 2021، صفحه 185-198 اصل مقاله (373.2 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20219.1060 | ||
| نویسنده | ||
| Xinyue Cheng* | ||
| School of Mathematical Sciences Chongqing Normal University Chongqing, China | ||
| چکیده | ||
| 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 definitions 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 $\mathrm{Ric}_{N}\geq K >0 $. | ||
| کلیدواژهها | ||
| Dual Finsler metric؛ Gradient vector field؛ Finsler Laplacian؛ Eigenvalue؛ Hessian؛ Lie derivative؛ Weighted Ricci curvature | ||
| مراجع | ||
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