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Advances in Mathematical Physics
Volume 2015, Article ID 808250, 6 pages
http://dx.doi.org/10.1155/2015/808250
Research Article

Orthogonal Projections Based on Hyperbolic and Spherical -Simplex

1Department of Mathematics, Faculty of Science, Gazi University, 06500 Ankara, Turkey
2Department of Mathematics, Art and Sciences Faculty, Nigde University, 51100 Nigde, Turkey

Received 4 December 2014; Accepted 23 February 2015

Academic Editor: Giorgio Kaniadakis

Copyright © 2015 Murat Savas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, NY, USA, 1983. View at MathSciNet
  2. B. Karlıga and A. T. Yakut, “Vertex angles of a simplex in hyperbolic space Hn,” Geometriae Dedicata, vol. 120, pp. 49–58, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. S. Izumiya and F. Tari, “Projections of hypersurfaces in the hyperbolic space to hyperhorospheres and hyperplanes,” Revista Matemática Iberoamericana, vol. 24, no. 3, pp. 895–920, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. H. Rieger, “Families of maps from the plane to the plane,” Journal of the London Mathematical Society. Second Series, vol. 36, no. 2, pp. 351–369, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  5. V. I. Arnol'd, “Singularities of systems of rays,” Russian Mathematical Surveys, vol. 38, no. 2, pp. 87–176, 1983. View at Publisher · View at Google Scholar
  6. J. W. Bruce, “Generic geometry, transversality and projections,” Journal of the London Mathematical Society, vol. 49, no. 1, pp. 183–194, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. W. Bruce, P. J. Giblin, and F. Tari, “Families of surfaces: height functions and projections to planes,” Mathematica Scandinavica, vol. 82, no. 2, pp. 165–185, 1998. View at Google Scholar · View at MathSciNet · View at Scopus
  8. B. Karol, Multidimensional Analytic Geometry, vol. 50, Instytut Matematyczay Polaskiej Akad. Nauk. To., Warsaw, Poland, 1969, translation from the Polish by Halina Spalinska.
  9. L. J. Alías, T. Kurose, and G. Solanes, “Hadamard-type theorems for hypersurfaces in hyperbolic spaces,” Differential Geometry and its Applications, vol. 24, no. 5, pp. 492–502, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. E. B. Vinberg, Geometry II, vol. 29 of Encyclopaedia of Mathematical Sciences, Springer, New York, NY, USA, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  11. A. D. Mednykh and M. G. Pashkevich, “Elementary formulas for a hyperbolic tetrahedron,” Siberian Mathematical Journal, vol. 47, no. 4, pp. 687–695, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. B. Karliğa, “Edge matrix of hyperbolic simplices,” Geometriae Dedicata, vol. 109, pp. 1–6, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. R. A. Brualdi and H. Schneider, “Determinantal identities: gauss, schur, cauchy, sylvester, kronecker, jacobi, binet, laplace, muir, and cayley,” Linear Algebra and its Applications, vol. 52-53, pp. 769–791, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  14. A. Ushijima, “The tilt formula for generalized simplices in hyperbolic space,” Discrete & Computational Geometry, vol. 28, no. 1, pp. 19–27, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus