15 citations · 73 across the 31 of their papers we have counts for
31 papers
Finsler manifolds with Positive Weighted Flag Curvature
Zhongmin Shen, Runzhong Zhao
The flag curvature is a natural Finsler extension of the sectional curvature in Riemannian geometry. However, there are many non-Riemannian quantities which interact with the flag…
On the Pontrjagin classes of spray manifolds
Zhongmin Shen, Runzhong Zhao
Locally projectively flat metrics (or sprays) form a rich class of metrics (or sprays) in Finsler and spray geometry. The characterization of such metrics is the Hilbert Fourth Pro…
On a Class of Weakly Weighted Einstein Metrics
Zhongmin Shen, Runzhong Zhao
Weighted Ricci curvatures with various weights of the S-curvature have played an important role in Finsler geometry, especially in the control of volumes of Finsler manifolds. In t…
Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below
Xinyue Cheng, Zhongmin Shen
We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop-Gromov type…
Ricci flat Finsler metrics by warped product
Patricia Marcal, Zhongmin Shen
In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, S. and Zhao (2018), with another "warping", one that is consistent with sta…
On sprays with vanishing X-curvature
Zhongmin Shen
Every Riemannian metric or Finsler metric on a manifold induces a spray via its geodesics. In this paper, we discuss several expressions for the X-curvature of a spray. We show tha…