Purdue University Graduate School
Thesis - Runzhong Zhao.pdf (578.8 kB)
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posted on 2023-08-30, 20:20 authored by Runzhong ZhaoRunzhong Zhao

The 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.


Degree Type

  • Doctor of Philosophy


  • Mathematics

Campus location

  • Indianapolis

Advisor/Supervisor/Committee Chair

Zhongmin Shen

Additional Committee Member 2

Olguta Buse

Additional Committee Member 3

Daniel Ramras

Additional Committee Member 4

Roland Roeder