极小浸入在单位球面中的完备黎曼流形

Complete Riemannian manifolds minimally immersed in S n+p (1)

给出单位球面中完备极小子流形的一些特征，推广了单位球面中紧致极小子流形的一个结果．即，设Ｍ是Ｓｎ＋ｐ（１）（ｐ＞１）中的ｎ维完备极小子流形，则Ｍ全测地，或Ｍ是Ｓ４的Ｖｅｒｏｎｅｓｅ曲面，或ｓｕｐ‖σ‖２＞２３ｎ．

The paper presents the generalization of the results due to Li Anmin and Li Jimin to complete Riemannian manifolds and gives some characterization of complete minimal submanifold of unit sphere S n+p (1). Thus, the following is obtained; Let M be an n dimensional complete minimal submanifold in S n+p (1)( p >1), then either M is totally geodesic or M is the Veronese surface in S 4 or sup‖σ‖ 2>23 n .