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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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 |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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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1807321793164214272 |