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Year 2015, Volume 3, 2015, 1 - 3, 26.05.2016

Abstract

References

  • Blumenthal, L.M., Theory and Applications of Distance Geometry, Chelsea Publishing Company, Bronx, New York, (1970).
  • Blumenthal, L.M., Metric Foundation of Hyperbolic Geometry, Revista de Ciencias, 40, 3-20, (1938).
  • Fenchel, W., Elementary Geometry in Hyperbolic Space, W.de Gruyter, Berlin, New York, (1989).
  • Karliga, B., Edge Matrix of Hyperbolic Simplices, Geometriae Dedicata, 109, 1-6, (2004).
  • Luo, F., On a problem of Fenchel, Geometriae Dedicata,64, 277-282, (1997).
  • O’neill, B., Semi-Riemannian Geometry, Academic Press, New York, (1983).
  • Ratcliffe, J.G., Foundations of Hyperbolic Manifold,Springer-Verlag, New York, (1994).
  • Schlenker, J.M., Dihedral Angles of Convex Polyhedra, Discrete Comput.Geom., 23, 409-417, (2000).
  • Schlenker, J.M., Hypersurfaces in Hn and the Space of Its Horospheres, Geometric and Functional Analysis, 12, 395-435, (2002).
  • Schlenker, J.M., M´etriques sur les Poly´edres Hyperboliques Convexes, J. Differential Geom., 48(2), 323-405, (1998).
  • Su´arez-Peir´o, E., A Schl¨afli Differential Formula for Simplices in Semi Riemannian Hyperquadrics, Pacific Journal of Mathematics, 194:1), 229-255, (2000).
  • Vinberg E.B., Geometry II, Encyclopaedia of Mathematical Sciences, Springer-Verlag, 29, Berlin, NewYork, (1993).

Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn

Year 2015, Volume 3, 2015, 1 - 3, 26.05.2016

Abstract

In this paper, we give necessary and sufficent conditions for n(n+1)/2 positive real numbers φij and θij to be dihedral angles and edge lengths of an n−simplex having spacelike faces with codimensions 1 and 2 in de Sitter space

References

  • Blumenthal, L.M., Theory and Applications of Distance Geometry, Chelsea Publishing Company, Bronx, New York, (1970).
  • Blumenthal, L.M., Metric Foundation of Hyperbolic Geometry, Revista de Ciencias, 40, 3-20, (1938).
  • Fenchel, W., Elementary Geometry in Hyperbolic Space, W.de Gruyter, Berlin, New York, (1989).
  • Karliga, B., Edge Matrix of Hyperbolic Simplices, Geometriae Dedicata, 109, 1-6, (2004).
  • Luo, F., On a problem of Fenchel, Geometriae Dedicata,64, 277-282, (1997).
  • O’neill, B., Semi-Riemannian Geometry, Academic Press, New York, (1983).
  • Ratcliffe, J.G., Foundations of Hyperbolic Manifold,Springer-Verlag, New York, (1994).
  • Schlenker, J.M., Dihedral Angles of Convex Polyhedra, Discrete Comput.Geom., 23, 409-417, (2000).
  • Schlenker, J.M., Hypersurfaces in Hn and the Space of Its Horospheres, Geometric and Functional Analysis, 12, 395-435, (2002).
  • Schlenker, J.M., M´etriques sur les Poly´edres Hyperboliques Convexes, J. Differential Geom., 48(2), 323-405, (1998).
  • Su´arez-Peir´o, E., A Schl¨afli Differential Formula for Simplices in Semi Riemannian Hyperquadrics, Pacific Journal of Mathematics, 194:1), 229-255, (2000).
  • Vinberg E.B., Geometry II, Encyclopaedia of Mathematical Sciences, Springer-Verlag, 29, Berlin, NewYork, (1993).
There are 12 citations in total.

Details

Other ID JA22SU96AV
Journal Section Articles
Authors

Baki Karliga This is me

Publication Date May 26, 2016
Published in Issue Year 2015 Volume 3, 2015

Cite

APA Karliga, B. (2016). Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn. Turkish Journal of Mathematics and Computer Science, 3(1), 1-3.
AMA Karliga B. Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn. TJMCS. May 2016;3(1):1-3.
Chicago Karliga, Baki. “Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn”. Turkish Journal of Mathematics and Computer Science 3, no. 1 (May 2016): 1-3.
EndNote Karliga B (May 1, 2016) Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn. Turkish Journal of Mathematics and Computer Science 3 1 1–3.
IEEE B. Karliga, “Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn”, TJMCS, vol. 3, no. 1, pp. 1–3, 2016.
ISNAD Karliga, Baki. “Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn”. Turkish Journal of Mathematics and Computer Science 3/1 (May 2016), 1-3.
JAMA Karliga B. Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn. TJMCS. 2016;3:1–3.
MLA Karliga, Baki. “Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn”. Turkish Journal of Mathematics and Computer Science, vol. 3, no. 1, 2016, pp. 1-3.
Vancouver Karliga B. Dihedral Angles and Edge Lengths of Spacelike n−simplex in Sn. TJMCS. 2016;3(1):1-3.