A new method to the study of the behavior of the geodesics on hyperbolic manifolds. Applications
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2022-12-30 13:22
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514.13:528.02 (1)
Geometry (103)
Geodesy. Surveying. Photogrammetry. Remote sensing. Cartography (112)
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BALCAN, Vladimir. A new method to the study of the behavior of the geodesics on hyperbolic manifolds. Applications. In: Competitivitatea şi Inovarea în Economia Cunoaşterii, Ed. 21, 28-29 septembrie 2018, Chișinău. Chisinau, Republica Moldova: Departamentul Editorial-Poligrafic al ASEM, 2018, Ediția 21, Vol.1, pp. 206-211. ISBN 978-9975-75-932-8.
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Competitivitatea şi Inovarea în Economia Cunoaşterii
Ediția 21, Vol.1, 2018
Conferința "Competitivitatea şi Inovarea în Economia Cunoaşterii"
21, Chișinău, Moldova, 28-29 septembrie 2018

A new method to the study of the behavior of the geodesics on hyperbolic manifolds. Applications

CZU: 514.13:528.02
MSC 2010: 53C60,30F60,53C22

Pag. 206-211

Balcan Vladimir
 
Academia de Studii Economice din Moldova
 
 
Disponibil în IBN: 16 ianuarie 2019


Rezumat

The presented work is a research in the field of the geometry of two-dimensional hyperbolic (equipped with a metric of constant negative curvature) manifolds. In this survey article we gather resent results of  the  global behavior of  geodesics  on hyperbolic manifolds, giving special attention to the two-dimensional case. This paper discribe new method (is developed a new method of colour multilaterals) for solving  this  problem - an algorithm (the construction of a practical approach) that allows determine the behavior of this geodesic on hyperbolic manifolds. With the help of this technique, the question of the qualitative behavior of geodesics in general on hyperbolic 2-manifolds is solved. Applications and future direction are discussed.

Cuvinte-cheie
behavior of geodesics, the multilateral, the method of colour multilaterals, hyperbolic right angled hexagon, hyperbolic right angled octagon, pair pants (meaning surfaces of signature (0,3)). hyperbolic surface with genus g, k puncture and n geodesic boundaries