1. Integral Geometry on Surfaces of Constant Negative Curvature
- Author
-
Lluís Santaló
- Subjects
52.0X ,Convex geometry ,General Mathematics ,Hyperbolic space ,Mathematical analysis ,Espais hiperbòlics ,Differential geometry of curves ,Absolute geometry ,Geometry ,Spherical geometry ,symbols.namesake ,Geometria integral ,Gaussian curvature ,symbols ,Geometry, Non-Euclidian ,Total curvature ,Integral geometry ,Constant (mathematics) ,Mathematics ,Geometria no euclidiana ,Hyperbolic spaces - Abstract
We use the expression Integral geometry in the sense given it by Blaschke in “Vorlesungen über Integrtüçeomelrie”. In a previous paper (“Integral formulas in Croflon style on the sphere and some inequalities referring to spherical curve” (1942), Duke Mathematical Journal, vol. 9, pp. 707) we generalized to the sphere many formulas of plane integral geometry and at the same time applied these to the demonstration of certain inequalities referring to spherical curves. The present paper considers analogous qüestions for surfaces of constant negative curvature and consequently for hyperbolic geometry https://doi.org/10.1215/S0012-7094-43-01064-6
- Published
- 1943