Dihedrons of a Hyperbolic Three-Space of Positive Curvature

Year 2016, , 50 - 58, 30.10.2016

Lyudmila N. Romakina

https://doi.org/10.36890/iejg.584585

Cited By: 3

Abstract

Keywords

hyperbolic three-space of positive curvature, dihedron of the hyperbolic three-space of positive curvature, measure of a dihedron, base of a dihedron

References

• [1] Cayley A., A Sixth memoir upon quantics. Phil. Trans. Roy. Soc. London. 149 (1859).
• [2] Efimov N. V., Higher Geometry. MAIK. Nauka/Interperiodika. FIZMATLIT, Moscow, 2004. (In Russian)
• [3] Klein F., Vergleichende Betrachtungen über neuere geometrische Forschungen, Programm zum Eintritt in die philosophische Facultat und den Senat der Universitat zu Erlangen. A. Deichert, Erlangen, 1872.
• [4] Klein F., Vorlesungen Über Nicht-Euclidische Geometrie. Verlag von Julius Springer, Berlin, 1928. [5] Laguerre, Sur la theorie des foyers. Nouv. Ann. de Mathem. 12 (1853), 57-66.
• [6] Richter-Gebert Jürgen, Perspectives on Projective Geometry: A Guided Tour Through Real and Complex. Springer Science + Business Media, New York, 2011.
• [7] Romakina L. N., Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature. Sib. Elektron.Mat. Izv. 10 (2013), 393-407. (In Russian)
• [8] Romakina L. N., Classification of tetrahedrons with not hyperbolic sides in a hyperbolic space of positive curvature. Chebyshevskii Sb. 16 (2015), no. 2, 208-221. (In Russian)
• [9] Romakina L. N., Geometries of the co-Euclidean and co-pseudoeuclidean planes. Saratov, Publishing house Scientific book, 2008. (In Russian)
• [10] Romakina L. N., Geometry of the hyperbolic plane of positive curvature. P. 1: Trigonometry. Saratov, Publishing House of the Saratov University, 2013. (In Russian)
• [11] Romakina L. N., Geometry of the hyperbolic plane of positive curvature. P. 2: Transformations and simple partitions. Saratov, Publishing House of the Saratov University, 2013. (In Russian)
• [12] Romakina L. N., The Area of a Generalized Polygon without Parabolic Edges of a Hyperbolic Plane of Positive Curvature. Asian Journal of Mathematics and Computer Research 10 (2016), no. 4, 293-310.
• [13] Rosenfeld B. A., Geometry Of Lie Groups. Springer Science + Business Media, New York, 2015.
• [14] Rosenfeld B. A., Non-Euclidean spaces. Nauka, Moscow, 1969. (In Russian)
• [15] Rosenfeld B. A., Zamahovsky M. P. Geometry of groups of Lie. Symmetric, parabolic and periodic spaces. Moscow, MCCME, 2003. (In Russian)
• [16] Young J. W., Projective Geometry. The Open Court Publishing Company, Chicago, Illinois, 1930.