The convexity radius of a Riemannian manifold
The convexity radius of a Riemannian manifold
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DOI：
10.4310/ajm.2017.v21.n1.a4
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发表时间：
2014-12
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影响因子：
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通讯作者：
James Dibble
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文献类型：
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作者：
James Dibble
凸性半径与内射性半径之比可以在任何固定维数至少为2的紧致黎曼流形类中任意小。这是证明使用格列佛的方法，建设流形的焦点，但没有共轭点。该方法建议的凸半径，类似于一个经典的结果Klingenberg的内射半径的表征。
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.