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.
Keywords
Conformal hyperbolic triangle Conformal hyperbolic isosceles triangle Conformal hyperbolic equilateral triangle
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.
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2020 |
| Submission Date | April 14, 2020 |
| Acceptance Date | September 1, 2020 |
| Published in Issue | Year 2020 |