Minimal total absolute curvature for immersions
Minimal total absolute curvature for immersions
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浸没的最小总绝对曲率
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
N. Kuiper
中科院分区：
文献类型：
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作者：
N. Kuiper
在欧氏空间中，绝对总曲率最小的闭流形的浸入或映射称为紧形。（它们在b[25]中被称为凸形。）在第1章的定义、第2章的许多例子和第3章的一些特殊主题之后，我们在第4章证明了n-球的拓扑紧浸入只是期望的类型，即嵌入到凸+1维体的边界上。这推广了光滑情况下Chern和Lashof的一个定理。在第五章中，我们证明了在任何欧几里得空间中存在许多没有紧光滑浸没的流形。
Immersions or maps of closed manifolds in Euclidean space, of minimal absolute total curvature are called tight in this paper. (They were called convex in [25].) After the definition in Chapter 1, many examples in Chapter 2, and some special topics in Chapter 3, we prove in Chapter 4 that topological tight immersions ofn-spheres are only of the expected type, namely embeddings onto the boundary of a convexn+1-dimensional body. This generalises a theorem of Chern and Lashof in the smooth case. In Chapter 5 we show that many manifolds exist that have no tight smooth immersion in any Euclidean space.