关于Finsler子流形的平均曲率

On the Mean Curvature of Finsler Submanifolds

通过使用由射影球丛诱导的体积元来研究Finsler子流形几何,推导了体积泛函的第一变分公式。给出了Finsler子流形的平均曲率形式和第二基本形式的定义,该定义在Riemannian情形下与通常的概念一致．此外,通过推导射影球丛纤维上的散度公式。给出了平均曲率形式的一种非常简洁的等价表示,并得到一些关于Minkowski空间中Finsler子流形的有趣的结果．

By using the volume form induced from the projective sphere bundle of the Finsler manifold, the Finsler geometry of submanifolds is studied. The first variation formula of the volume functional for Finsler submanifolds is derived. The second fundamental form and the mean curvature form for Finsler submanifolds are defined, which coincide with the usual notions for the Riemannian case. By deriving the divergence formula on the fiber of the projective sphere bundle, a simple equivalence expression of the mean curvature form is given. Some interesting results for Finsler submanifolds in the Minkowski space are established.