Finsler几何中体积形式与子流形

On the Volume Forms and Submanifolds in Finsler Geometry

本文对一般的Finsler体积元讨论了Finsler子流形几何,证明了关于任意Finsler体积元, Minkowski空间中不存在闭定向的极小子流形,关键在于对任意的Finsler体积元,沈忠民的方法仍然有效．对于特殊Randers空间中的子流形,给出了其体积增长估计,从而得到了Randers空间可以极小浸入到特殊Randers空间的一个必要条件．

This paper studies the Finsler geometry of submanifolds with respect to general Finsler volume element. The key is that Shen＇s method still works in dealing with any other Finsler volume element, and prove that there exists no closed oriented minimal submanifold in Minkowski space with respect to any Finsler volume element, and also obtain an estimate of volume growth for submanifolds in special Randers space and thus provides a necessary condition for a Randers space to be minimally immersed into special Randers space.