The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula

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• 作者：Nan Ye ; Xiang Ma ; Donghao Wang
• 关键词：Strong ; spacelike curves ; Fenchel theorem ; Fary ; Milnor theorem ; Total curvature ; Crofton formula
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：50
• 期：3
• 页码：249-259
• 全文大小：628 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Mathematical and Computational Physics
  Group Theory and Generalizations
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9060
• 卷排序：50

文摘

We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the total curvatures must be less than or equal to \(2\pi \). A similar generalization of the Fary-Milnor theorem is also obtained. We establish the Crofton formula on the de Sitter 2-sphere which implies the above results.