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Dihedrons of a Hyperbolic Three-Space of Positive Curvature

Year 2016, Volume: 9 Issue: 2, 50 - 58, 30.10.2016
https://doi.org/10.36890/iejg.584585

Abstract

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.
Year 2016, Volume: 9 Issue: 2, 50 - 58, 30.10.2016
https://doi.org/10.36890/iejg.584585

Abstract

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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Lyudmila N. Romakina

Publication Date October 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 2

Cite

APA Romakina, L. N. (2016). Dihedrons of a Hyperbolic Three-Space of Positive Curvature. International Electronic Journal of Geometry, 9(2), 50-58. https://doi.org/10.36890/iejg.584585
AMA Romakina LN. Dihedrons of a Hyperbolic Three-Space of Positive Curvature. Int. Electron. J. Geom. October 2016;9(2):50-58. doi:10.36890/iejg.584585
Chicago Romakina, Lyudmila N. “Dihedrons of a Hyperbolic Three-Space of Positive Curvature”. International Electronic Journal of Geometry 9, no. 2 (October 2016): 50-58. https://doi.org/10.36890/iejg.584585.
EndNote Romakina LN (October 1, 2016) Dihedrons of a Hyperbolic Three-Space of Positive Curvature. International Electronic Journal of Geometry 9 2 50–58.
IEEE L. N. Romakina, “Dihedrons of a Hyperbolic Three-Space of Positive Curvature”, Int. Electron. J. Geom., vol. 9, no. 2, pp. 50–58, 2016, doi: 10.36890/iejg.584585.
ISNAD Romakina, Lyudmila N. “Dihedrons of a Hyperbolic Three-Space of Positive Curvature”. International Electronic Journal of Geometry 9/2 (October 2016), 50-58. https://doi.org/10.36890/iejg.584585.
JAMA Romakina LN. Dihedrons of a Hyperbolic Three-Space of Positive Curvature. Int. Electron. J. Geom. 2016;9:50–58.
MLA Romakina, Lyudmila N. “Dihedrons of a Hyperbolic Three-Space of Positive Curvature”. International Electronic Journal of Geometry, vol. 9, no. 2, 2016, pp. 50-58, doi:10.36890/iejg.584585.
Vancouver Romakina LN. Dihedrons of a Hyperbolic Three-Space of Positive Curvature. Int. Electron. J. Geom. 2016;9(2):50-8.