| Although the differential geometry of minimal surfaces in Riemannian manifolds has been extensively developed,minimal surfaces in Finsler spaces have not been studied and developped at the same pace.There are still few examples about minimal submanifolds.Zhongmin Shen introduced the notion of mean curvature into Finsler manifolds by taking the first-order variation on the volume functional.Here this paper bases on the work of Ningwei Cui and Linfeng Zhou,and studies the minimal submanifolds under the Berwald’s square metric.By viewing the square metric as a spherically symmetric metric,we calculate the mean curvature of graphs and surfaces of revolution under both Busemann-Hausdorff measure and Holmes-Thompson measure when the ambient space is 3 dimensional Berwald’s square metric manifold,and then prove that the sphere has the same mean curvature,which is constant,under both measures.In addition,we prove that for any dimension there exists no closed oriented minimal submanifolds. |
