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Equality of internal angles and vertex points in conformal hyperbolic triangles

Year 2020, Volume: 41 Issue: 3, 642 - 650, 30.09.2020
https://doi.org/10.17776/csj.719117

Abstract

In this article, by using the conformal structure in Euclidean space, the conformal structures in hyperbolic space and the equality of the internal angles and vertex points of conformal triangles in hyperbolic space are given. Especially in these special conformal triangles, the conformal hyperbolic equilateral triangle and the conformal hyperbolic isosceles triangle, the internal angles and vertices are shown.

References

  • Asmus, I., Duality Between Hyperbolic and de-Sitter Geometry, Cornell University, New York, (2008) 1-32.
  • O’neil, B., Semi-Riemannian Geometry, Academic Press., London, (1983) 46-49, 54-57, 108-114, 143-144.
  • Suarez-Peiro, E., A Schlafli Differential Formula for Implices in Semi-Riemannian Hyperquadrics, Gauss-Bonnet Formulas for Simplices in the de Sitter Sphere and the Dual Volume of a Hyperbolic Simplex, Pasicif Journal of Mathematics, 194(1) (2000) 229.
  • Karlığa, B., Edge matrix of hyperbolic simplices, Geom. Dedicata, 109 (2004) 1–6.
  • Karlığa, B., Yakut, A.T., Vertex angles of a simplex in hyperbolic space , Geom. Dedicata, 120 (2006) 49-58.
  • Alsan, Ö., Conformal Triangles, M.Sc. Thesis, Kastamonu University Institute of Science and Technology, Kastamonu 2015.
  • Karlığa, B., Savaş, M., “Field Formulas Based on Edge Lengths of Hyperbolic and Spherical Triangles”, Seminar of Mathematics Deparment, Gazi University, Ankara, (2006) 1-6.
  • Ratcliffe, J.G., “Foundations of Hyperbolic Manifolds”, Springer-Verlag, Berlin, (1994).
  • Tokeşer, Ü., “Triangles in Spherical Hyperbolic and de-Sitter Planes”, Ph.D. Thesis, Gazi University Institute of Science and Technology, Ankara 2013.
Year 2020, Volume: 41 Issue: 3, 642 - 650, 30.09.2020
https://doi.org/10.17776/csj.719117

Abstract

References

  • Asmus, I., Duality Between Hyperbolic and de-Sitter Geometry, Cornell University, New York, (2008) 1-32.
  • O’neil, B., Semi-Riemannian Geometry, Academic Press., London, (1983) 46-49, 54-57, 108-114, 143-144.
  • Suarez-Peiro, E., A Schlafli Differential Formula for Implices in Semi-Riemannian Hyperquadrics, Gauss-Bonnet Formulas for Simplices in the de Sitter Sphere and the Dual Volume of a Hyperbolic Simplex, Pasicif Journal of Mathematics, 194(1) (2000) 229.
  • Karlığa, B., Edge matrix of hyperbolic simplices, Geom. Dedicata, 109 (2004) 1–6.
  • Karlığa, B., Yakut, A.T., Vertex angles of a simplex in hyperbolic space , Geom. Dedicata, 120 (2006) 49-58.
  • Alsan, Ö., Conformal Triangles, M.Sc. Thesis, Kastamonu University Institute of Science and Technology, Kastamonu 2015.
  • Karlığa, B., Savaş, M., “Field Formulas Based on Edge Lengths of Hyperbolic and Spherical Triangles”, Seminar of Mathematics Deparment, Gazi University, Ankara, (2006) 1-6.
  • Ratcliffe, J.G., “Foundations of Hyperbolic Manifolds”, Springer-Verlag, Berlin, (1994).
  • Tokeşer, Ü., “Triangles in Spherical Hyperbolic and de-Sitter Planes”, Ph.D. Thesis, Gazi University Institute of Science and Technology, Ankara 2013.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Ümit Tokeşer 0000-0003-4773-8291

Ömer Alsan 0000-0002-6535-5174

Publication Date September 30, 2020
Submission Date April 14, 2020
Acceptance Date September 1, 2020
Published in Issue Year 2020Volume: 41 Issue: 3

Cite

APA Tokeşer, Ü., & Alsan, Ö. (2020). Equality of internal angles and vertex points in conformal hyperbolic triangles. Cumhuriyet Science Journal, 41(3), 642-650. https://doi.org/10.17776/csj.719117