arXiv subjects

Runzhong Zhao

Publications and source records attributed to Runzhong Zhao.

4 recordsLinked to original sources

arXiv2023

Finsler manifolds with Positive Weighted Flag Curvature

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 curvature. In this paper, we introduce a notion of weighted flag curvature by modifying the flag curvature using the non-Riemannian quantity, $T$-curvature. We show that a forward complete open Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, and that a compact Finsler manifold with nonnegative weighted flag curvature and strictly convex boundary is diffeomorphic to a Euclidean ball.

math.DG↗

arXiv2022

On a Class of Weakly Weighted Einstein Metrics

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 this paper, we study general weighted Ricci curvatures, and characterize Randers metrics of almost isotropic weighted Ricci curvatures.

math.DG↗

arXiv2022

On the Pontrjagin classes of spray manifolds

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 Problem in the regular case. In this paper we study the Pontrjagin classes of a manifold given a spray structure, and show that a manifold equipped with a locally projectively flat Finsler metric (or spray) has zero Pontrjagin classes.

math.DG↗

arXiv2017

Ultrasound attenuation in $s^\pm$-wave two-band superconductors

The two-band $s^{\pm}$-wave state is currently considered to be the most promising candidate for newly discovered iron-based high-$T_c$ superconductors. In this work we study theoretically the ultrasound attenuation in $s^{\pm}$-wave two-band superconductors. The impurity effect is calculated within the $\mathcal{T}$-matrix approximation. In particular, our theory predict that, when the sizes of two order parameter are comparable, a Hebel-Slichter peak may show up in the ultrasound attenuation versus temperature curves. Our calculations also confirmed the presence of the resonant impurity scattering at low temperature, observed previously by other authors in the calculation of the NMR relaxation rate $1/T_{1}$.

cond-mat.supr-con↗