Tight and Taut Submanifolds
Tight and Taut Submanifolds
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紧绷子流形
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
S. Chern
中科院分区：
文献类型：
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作者：
Thomas E. Cecil;S. Chern
紧子流形和紧子流形是一类重要的具有特殊曲率性质的流形，自20世纪50年代以来，微分几何学者对其进行了深入的研究。在某些方面，它们是凸体之后最简单的图形：例如，R^n中的紧流形的特征在于它们与任何半空间的交点都是连通的。例子包括许多众所周知的流形，如球体、维罗内曲面、等参超曲面和杜平环。
Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. They are in some ways the simplest figures after convex bodies: for example, tight manifolds in R^n are characterized by the fact that their intersection with any half-space is connected. Examples include many well-known manifolds such as spheres, Veronese surfaces, isoparametric hypersurfaces and the cyclides of Dupin.