Weighted Curvatures in Finsler Geometry

dc.contributor.advisorShen, Zhongmin
dc.contributor.authorZhao, Runzhong
dc.contributor.otherBuse, Olguta
dc.contributor.otherRamras, Daniel
dc.contributor.otherRoeder, Roland
dc.date.accessioned2023-08-31T17:18:38Z
dc.date.available2023-08-31T17:18:38Z
dc.date.issued2023-08
dc.degree.date2023
dc.degree.disciplineMathematical Sciencesen
dc.degree.grantorPurdue University
dc.degree.levelPh.D.
dc.descriptionIndiana University-Purdue University Indianapolis (IUPUI)en
dc.description.abstractThe curvatures in Finsler geometry can be defined in similar ways as in Riemannian geometry. However, since there are fewer restrictions on the metrics, many geometric quantities arise in Finsler geometry which vanish in the Riemannian case. These quantities are generally known as non-Riemannian quantities and interact with the curvatures in controlling the global geometrical and topological properties of Finsler manifolds. In the present work, we study general weighted Ricci curvatures which combine the Ricci curvature and the S-curvature, and define a weighted flag curvature which combines the flag curvature and the T -curvature. We characterize Randers metrics of almost isotropic weighted Ricci curvatures and show the general weighted Ricci curvatures can be divided into three types. On the other hand, we show that a proper open forward complete Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, generalizing the Gromoll-Meyer theorem in Riemannian geometry.
dc.identifier.urihttps://hdl.handle.net/1805/35287
dc.language.isoen_US
dc.rightsAttribution-NonCommercial 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/
dc.subjectFinsler metrics
dc.subjectWeighted Ricci curvature
dc.subjectWeighted flag curvature
dc.subjectWeighted Einstein Metrics
dc.titleWeighted Curvatures in Finsler Geometry
dc.typeThesisen
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