Birman, Graciela Silvia About the densities for straight lines in semi-Riemannian spaces. (English) Zbl 1190.53072 J. Geom. Symmetry Phys. 14, 1-11 (2009). The author considers some families of all linear \(r\)-subspaces of a given \(n\)-dimensional space. The aim is to find the densities of such families, which are \((n-r)(r+1)\)-differential forms.First, for \(n=3\), the cases \(r=2\) and \(r=1\) are considered, and the corresponding densities are computed in the Euclidean space.For \(n=2\) and \(r=1\) the density is determined in the case of a semi-Riemannian space. From this, new formulas can be derived for the particular cases of Euclidean and Lorentzian plane.Further, the density for the family of lines which are tangent to a differentiable curve in the Euclidean plane is obtained as a function of the curvature of the curve.Also, the family of planes which are tangent to a differential surface is considered, and its density is computed in terms of the Hessian of the surface itself Reviewer: Paolo Dulio (Milano) Cited in 1 Document MSC: 53C65 Integral geometry Keywords:curvature; density; Hessian; semi-Riemannian space × Cite Format Result Cite Review PDF