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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Autor principal: Birman, G.S.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00465755_v15_n4_p399_Birman
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spelling todo:paper_00465755_v15_n4_p399_Birman2023-10-03T14:52:16Z Crofton's and poincaré's formulas in the Lorentzian plane Birman, G.S. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Birman, G.S.
spellingShingle Birman, G.S.
Crofton's and poincaré's formulas in the Lorentzian plane
author_facet Birman, G.S.
author_sort Birman, G.S.
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
url http://hdl.handle.net/20.500.12110/paper_00465755_v15_n4_p399_Birman
work_keys_str_mv AT birmangs croftonsandpoincaresformulasinthelorentzianplane
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