Weighted Ricci curvature in Riemann-Finsler geometry
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 vi...
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| Format: | Article |
| Language: | English |
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Amirkabir University of Technology
2021-09-01
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| Series: | AUT Journal of Mathematics and Computing |
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| Online Access: | https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf |
| Summary: | 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. |
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| ISSN: | 2783-2449 2783-2287 |