Tipuri de geodezice pe varietăţi hiperbolice
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2022-12-13 08:35
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BALCAN, Vladimir. Tipuri de geodezice pe varietăţi hiperbolice. In: Competitivitatea şi inovarea în economia cunoaşterii, Ed. Vol. 1. – 2015. , 25-26 septembrie 2015, Chișinău. Chisinau, Republica Moldova: Departamentul Editorial-Poligrafic al ASEM, 2015, Vol.1, pp. 172-182. ISBN 978-9975-75-714-0.
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Competitivitatea şi inovarea în economia cunoaşterii
Vol.1, 2015
Simpozionul "Competitivitatea şi inovarea în economia cunoaşterii"
Vol. 1. – 2015. , Chișinău, Moldova, 25-26 septembrie 2015

Tipuri de geodezice pe varietăţi hiperbolice


Pag. 172-182

Balcan Vladimir
 
Academia de Studii Economice din Moldova
 
Disponibil în IBN: 11 decembrie 2018


Rezumat

We are concerned in this paper with the behavior in the large of the geodesic lines on hyperbolic twodimensional hyperbolic manifolds (surfaces). We sketch some methods to study the global behaviour of launched geodesics on hyperbolic 2-manifolds. With geodesic we mean here the shortest path between two points compared to all neighboring paths. With geodesics we mean such local minima. Here by a geodesic we always mean a locally shortest curve. The study of geodesics on surfaces can be reduced to the study of curves on a pair of pants. Compact hyperbolic surfaces can be seen as an elementary pasting of geodesic polygons of the hyperbolic plane. Conversely, cutting such a surface along disjoint simple closed geodesics (a partition), one obtains a family of pair of pants (surfaces of signature (0,3)), which in turn can be readily cut to obtain a pair of isometric right-angled hexagons. We examining different types of behaviours exhibited by geodesics on a given pair of hyperbolic pants. We also allow the degenerate case in which one or more of the lenths vanish. We call a generalized pair of pants a hyperbolic surface which is a homeomorphic to a sphere with three holes, a hole being either a geodesic boundary component or a cusp.

Cuvinte-cheie
Hyperbolic manifolds, complete simple geodesics, spiralling geodesics, simple orthogeodesic arcs, gap region, simple ideal geodesics (bi-infinite), simple infinite geodesic rays, lasso, cusp, pair of pants with a cusp, thrice-punctured sphere.