THE BEHAVIOR OF GEODESICS IN TWO-DIMENSIONAL HYPERBOLIC MANIFOLDS - DE

The main purpose of this work is the given a new constructive method for solving the problem of the behavior of geodesic on hyperbolic surfaces of genus g, k punctures and with n geodesic boundary components. At first:1) we obtain a complete classification of all possible geodesic curves on the simplest hyperbolic 2-manifolds (hyperbolic horn; hyperbolic cylinder; parabolic horn (cusp), hyperbolic pants); 2) on surface of genus 2; Finally: 3) on compact closed hyperbolic surface without boundarie (general case); 4) on hyperbolic surface of genus g and with n geodesic boundary components; 5) on hyperbolic 1-punctured torus; on generalized hyperbolic pants; in general case: for any punctured hyperbolic surface of genus g and k punctures; 6) in the most general case: or in any hyperbolic surface of genus g, k punctures and with n boundary curves.

Product details

• Authors: Vladimir Balcan
• Publisher: LAP Lambert Academic Publishing
• Languages: English
• Product format: Paperback / Softback
• Released: 18.07.2023
• EAN: 9786206751267
• ISBN: 9786206751267
• No. of pages: 52
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous