The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula
| Autor: | Nan Ye, Xiang Ma, Donghao Wang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Crofton formula 010102 general mathematics Curvature 01 natural sciences 010104 statistics & probability General Relativity and Quantum Cosmology Differential Geometry (math.DG) Differential geometry Lorentz space De Sitter universe 52A40 53C50 53C65 FOS: Mathematics Total curvature Geometry and Topology Tangent vector Mathematics::Differential Geometry 0101 mathematics Fary–Milnor theorem Analysis Mathematics Mathematical physics |
| Popis: | 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. Comment: 9 pages, 4 figures. Comments are welcome |
| Databáze: | OpenAIRE |
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