期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1991
卷号：14
DOI：10.1155/S0161171291000728
出版社：Hindawi Publishing Corporation
摘要：The object of the paper is to study some compact
submanifolds in the Euclidean space Rn whose mean curvature
vector is parallel in the normal bundle. First we prove that
there does not exist an n-dimensional compact simply connected
totally real submanifold in R2n whose mean curvature vector is
parallel. Then we show that the n-dimensional compact totally
real submanifolds of constant curvature and parallel mean
curvature in R2n are flat. Finally we show that compact
Positively curved submanifolds in Rn with parallel mean
curvature vector are homology spheres. The last result in
particular for even dimensional submanifolds implies that their
Euler poincaré characteristic class is positive, which for the
class of compact positively curved submanifolds admiting isometric
immersion with parallel mean curvature vector in Rn, answers the
problem of Chern and Hopf
