Crofton's and Poincaré's formulas in the Lorentzian plane
type: Item
instance of: scholarly article
title: Crofton's and Poincaré's formulas in the Lorentzian plane
zbMATH Open document ID: 0538.53066
DOI: 10.1007/BF00211708
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: The author gives the densities for points and lines (geodesics), the kinematic density and the density for pairs of points and pairs of lines in the sense of integral geometry, for the Lorentzian plane \((ds^ 2=dx^ 2-dy^ 2)\). Then, it is shown that Crofton's and Poincaré's classical formulas hold for piecewise pure curves (i.e. curves whose tangent vectors at every point are timelike or spacelike) with certain limitations for the angles between the curves and the intersection lines or between the intersection curves.
reviewed by: L. A. Santaló
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 3855948
zbMATH Keywords: Crofton formula
zbMATH Keywords: Poincaré formula
zbMATH Keywords: kinematic density
zbMATH Keywords: Lorentzian plane
author: Graciela S. Birman
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00211708
OpenAlex ID: W1974073964
description: scientific article; zbMATH DE number 3855948