Crofton's and poincaré's formulas in the Lorentzian plane
The purpose of the present paper is to compare some of the formulas of integral geometry in the Euclidean plane with those for the Lorentzian plane. In particular, we find that the so-called Crofton's formula and Poincaré's formula hold only under the restrictions expressed in Theorems 1 a...
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1984
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00465755_v15_n4_p399_Birman http://hdl.handle.net/20.500.12110/paper_00465755_v15_n4_p399_Birman |
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| Sumario: | The purpose of the present paper is to compare some of the formulas of integral geometry in the Euclidean plane with those for the Lorentzian plane. In particular, we find that the so-called Crofton's formula and Poincaré's formula hold only under the restrictions expressed in Theorems 1 and 2, respectively. In order to arrive at these results, we find several different expressions for the density of geodesics and kinematic density. © 1984 D. Reidel Publishing Company. |
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