DOI QR코드

DOI QR Code

THE LINE ELEMENT APPROACH FOR THE GEOMETRY OF POINCARÉ DISK

  • Kim, Jong Ryul (Department of Mathematics, Kunsan National University)
  • Received : 2021.01.20
  • Accepted : 2021.06.14
  • Published : 2021.09.25

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

References

  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. https://doi.org/10.1006/jmaa.2000.7280
  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. https://doi.org/10.1016/j.jmaa.2017.07.012
  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. https://doi.org/10.1016/S0898-1221(01)85012-4