Browse > Article
http://dx.doi.org/10.5831/HMJ.2021.43.3.385

THE LINE ELEMENT APPROACH FOR THE GEOMETRY OF POINCARÉ DISK  

Kim, Jong Ryul (Department of Mathematics, Kunsan National University)
Publication Information
Honam Mathematical Journal / v.43, no.3, 2021 , pp. 385-402 More about this Journal
Abstract
The geometry of Poincaré disk itself is interpreted without any mapping to different spaces. Our approach might be one of the shortest and is intended for educational contribution.
Keywords
Poincare disk; inner product; cross ratio; holomorphic function; angle; line element;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. S. Birman and A. A. Ungar, The hyperbolic derivative in the Poincare ball model of hyperbolic geometry, J. Math. Anal. Appl. 254 (2001), 321-333.   DOI
2 N. V. Efimov, Higher geometry, Mir Publishers, 1980.
3 J. R. Kim, Python data analysis matrix mathematics, Kyungmoon Press, 2020.
4 John McCleary, Geometry from a Differentiable Viewpoint, Cambrige university press, 1994.
5 Barrett O' Neill, Elementary Differential Geometry 2nd edition, Academic press, 1997.
6 G. Popescu, Hyperbolic geometry on noncommutative polyballs, J. Math. Anal. Appl. 456 (2017), 576-607.   DOI
7 James R. Smart, Modern geometries 5th edition, Brooks/Cole Publishing Company, 1998.
8 A. A. Ungar, Hyperbolic trigonometry and its application in the Poincare ball model of hyperbolic geometry, Comput. Math. Appl., 41 (2001), 135-147.   DOI