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Weighted Ricci curvature in Riemann-Finsler geometry | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 2، شماره 2، آذر 2021، صفحه 117-136 اصل مقاله (396.15 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20473.1067 | ||
| نویسنده | ||
| Zhongmin Shen* | ||
| Department of Mathematical Sciences, Indiana University-Purdue University, 402 N Blackford Street, Indianapolis, IN 46202, USA | ||
| چکیده | ||
| Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. | ||
| کلیدواژه‌ها | ||
| Ricci curvature؛ $S$-curvature؛ Mean curvature | ||
| مراجع | ||
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[11] S. Yin, Two compactness theorems on Finsler manifolds with positivr weighted Ricci cirvature, Results Math, (2017). DOI 10.1007/s00025-017-0673-9 .
[12] S. Yin, Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below Frontiers of Mathematics in China 13(4) (2018), 1-14.
[13] G. Wei and W. Wylie, Comprison Geometry for the Bakry-Emery Ricci Tensor, J. Diff. Geom. 83 (2009), 377-405. | ||
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