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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Detalles Bibliográficos
Autor principal: Birman, Graciela Silvia
Publicado: 1984
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00465755_v15_n4_p399_Birman
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spelling paper:paper_00465755_v15_n4_p399_Birman2023-06-08T15:05:31Z Crofton's and poincaré's formulas in the Lorentzian plane Birman, Graciela Silvia 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. Fil:Birman, G.S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1984 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
author Birman, Graciela Silvia
spellingShingle Birman, Graciela Silvia
Crofton's and poincaré's formulas in the Lorentzian plane
author_facet Birman, Graciela Silvia
author_sort Birman, Graciela Silvia
title Crofton's and poincaré's formulas in the Lorentzian plane
title_short Crofton's and poincaré's formulas in the Lorentzian plane
title_full Crofton's and poincaré's formulas in the Lorentzian plane
title_fullStr Crofton's and poincaré's formulas in the Lorentzian plane
title_full_unstemmed Crofton's and poincaré's formulas in the Lorentzian plane
title_sort crofton's and poincaré's formulas in the lorentzian plane
publishDate 1984
url 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
work_keys_str_mv AT birmangracielasilvia croftonsandpoincaresformulasinthelorentzianplane
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