n.歧管(汽车引擎用以进气和排气)
adj.多的，多种多样的，许多种类的
vt.复写，复印，增多，使…多样化

原形：manifold第三人称单数：manifolds复数：manifolds过去式：manifolded过去分词：manifolded现在分词：manifolding

The surface of a sphere is a two-dimensional manifold embedded in three-dimensional space.
球面是一个嵌入在三维空间中的二维流形。
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
数学中，流形是在每一点邻域上都局部类似于欧几里得空间的拓扑空间。
The torus is a popular example of a compact manifold without boundary.
扭曲环面是一个没有边界的紧致流形的典型例子。
Riemannian manifolds generalize the notion of curvature to higher dimensions.
黎曼流形将曲率的概念推广到了高维空间。
Differentiable manifolds form the basis for much of modern differential geometry and physics, including general relativity.
可微流形是现代微分几何和物理学，包括广义相对论的基石。
The study of Lie groups involves both group theory and the geometry of smooth manifolds.
李群的研究结合了群论与光滑流形的几何学。
Manifolds with complex structures, known as complex manifolds, play a central role in algebraic geometry.
具有复结构的流形，即复流形，在代数几何中扮演着核心角色。
The Poincaré conjecture, proved by Grigori Perelman, states that every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
格里戈里·佩雷尔曼证明的庞加莱猜想表明，每一个单连通的闭合三维流形同胚于三维球面。
Fiber bundles are a formalization of the idea of a space with a differentiable structure on its fibers, which are themselves manifolds.
纤维丛是对一类空间形式化的表述，这类空间在其纤维上具有可微结构，而这些纤维本身也是流形。
Morse theory studies how the topology of a manifold changes as a function on it varies.
莫尔斯理论研究当定义在流形上的函数变化时，该流形的拓扑结构如何改变。