【摘要】 从子流形几何的观点出发 ,得到了关于单位球面中偶维数子流形 Mn 的一个拓扑球定理 .例子表明该结果是最佳的 .这个球定理与 Th.Vlachos最近的一个结果相对 ,他得到了球面中奇维数子流形的一个球定理 ,其关于维数的假定是本质的 .更多还原

【Abstract】 A topological sphere theorem from the point of view of submanifold geometry for even-dimensional submanifolds M n in the unit sphere is established.There are some examples which show that the result is optimal.This sphere theorem is the counterpart of the very recent result of Th.Vlachos who obtained such a sphere theorem for odd-dimensional submanifolds and his assumption on the dimension is essential.更多还原