Finsler流形的强极小子流形

Strongly minimal submanifold of Finsler manifold

摘要:

对于Finsler流形间非蜕化的光滑映射，我们利用射影球丛纤维上的散度公式给出了其能量泛函第一变分公式的另一种简洁的证明。同时，给出了Randers 空间中子流形关于Finsler度量和黎曼度量的第二基本形式，以及平均曲率向量场之间的关系。最后，给出了Randers 空间中强极小子流形的一个分类定理。

Abstract:

For the nondegenerate smooth map between manifolds, by using the divergence formula on fibre of the projective sphere bundle, another simpler way to prove the first variation formula of the energy functional is given. At the same time, the relations between the second fundamental forms (resp. the mean curvature) of Finsler metric and that of Riemannian metric in Randers spaces are discussed. At last, a classification theorem of strongly minimal submanifolds in Randers spaces is given.