arXiv subjects

Yi-Bing Shen

Publications and source records attributed to Yi-Bing Shen.

3 recordsLinked to original sources

arXiv2016

Nontrivial minimal surfaces in a hyperbolic Randers space

The contribution of this paper is two-fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing field, by considering the Busemann-Hausdorff measure and Holmes-Thompson measure simultaneously. The second one is to obtain the explicit local expressions of two types of nontrivial rotational BH-minimal surfaces in a Randers domain of constant flag curvature $K=-1$, which are the first examples of BH-minimal surfaces in the hyperbolic Randers space.

math.DG↗

arXiv2012

On Einstein Matsumoto metrics

In this paper, the necessary and sufficient conditions for Matsumoto metrics $F=\frac{α^2}{α-β}$ to be Einstein are given. It is shown that if the length of $β$ with respect to $α$ is constant, then the Matsumoto metric $F$ is an Einstein metric if and only if $α$ is Ricci-flat and $β$ is parallel with respect to $α$. A nontrivial example of Ricci flat Matsumoto metrics is given.

math.DG↗

arXiv2012

On Einstein Kropina metrics

In this paper, a characteristic condition of Einstein Kropina metrics is given. By the characteristic condition, we prove that a non-Riemannian Kropina metric $F=\frac{α^2}β$ with constant Killing form $β$ on an n-dimensional manifold $M$, $n\geq 2$, is an Einstein metric if and only if $α$ is also an Einstein metric. By using the navigation data $(h,W)$, it is proved that an n-dimensional ($n\geq2$) Kropina metric $F=\frac{α^2}β$ is Einstein if and only if the Riemannian metric $h$ is Einstein and $W$ is a unit Killing vector field with respect to $h$. Moreover, we show that every Einstein Kropina metric must have vanishing S-curvature, and any conformal map between Einstein Kropina metrics must be homothetic.

math.DG↗