one-dimensional manifold [数] 一维流形
three-dimensional manifold [数] 三维流形
closed two-dimensional manifold [数] 闭二维流形
High-dimensional manifold topology 高维流形拓扑学
open two-dimensional manifold [数] 开二维流形
dimensional manifold 维流形上
Some estimates of Gaussian curvature of conformal metric of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature were obtained.
给出了拟常曲率流形中二维极小子流形的共形度量的高斯曲率之上界估计。
Sufficient conditions for a simply-connected domain of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature to be stable were proved.
证明了拟常曲率流形中二维极小子流形上一个单连通区域为稳定的充分条件。
However, when the underlying lower-dimensional manifold is self-intersecting at some points, it's difficult to obtain local lower-dimensional structure from the Euclidean neighborhoods.
然而，当高维数据所逼近或近似的一个低维流形自相交时，欧氏距离意义上的邻域不能完全反映低维点的相邻关系，往往难以体现真实的局部线性结构。
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