Convexidad en el plano hiperbólico
dc.contributor.author
dc.date.accessioned
2009-07-17T07:48:30Z
dc.date.available
2009-07-17T07:48:30Z
dc.date.created
1969
dc.identifier.citation
Santaló, L. (1969). Convexidad en el plano hiperbolico. Revista de la Universidad Nacional de Tucumán: Serie A: Matemática y Física Teórica, 19 (1-2), 173-183
dc.identifier.issn
0080-2360
dc.identifier.uri
dc.description.abstract
A set of points Q in the hyperbolic plane is said to be h-convex (convex with respect to horocycles) if for each pair of points A, B belonging to Q, the entire segments of the two horocycles determined by A, B belong to Q. In this paper we give the following properties for h-convex sets: 1. If Q is an h- convex, the whole horocyclic lentil bounded by the horocycles O, O' determined by two points A, B of Q belongs to Q and we get the inequalities (2 . 8) between the length L of the boundary Q, the area F, the width A and the diameter D of Q. 2. If kg. denotes the geodesic curvature of the boundary Q of a set Q, then Q is an h-convex if and only if xg > 1. 3. For each point A of the boundary ‘Q of an h-convex set Q we consider the two tangent horocycles O- and O+ and define the breadth of Q with respect to each of them. These h-breadths O-, n+ satisfies the formulae (5.3) and (5.4). 4. The sets of constant breadth are considered specially. For them the formula (6.1) holds the last theorem states that the Reuleaux triangle has minimal length and minimal area among all the sets of the same constant breadth of the hyperbolic plane
dc.format.mimetype
application/pdf
dc.language.iso
Espanyol
dc.publisher
Facultad de Ciencias Exactas y Tecnología de la Universidad Nacional de Tucumán
dc.relation.ispartof
Revista de la Universidad Nacional de Tucumán: Serie A: Matemática y Física Teórica, 1969, vol. XIX, núm. 1-2, p. 173-183
dc.relation.ispartofseries
Publicacions
dc.rights
Tots els drets reservats
dc.subject
dc.title
Convexidad en el plano hiperbólico
dc.type
Article
dc.rights.accessRights
info:eu-repo/semantics/openAccess