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RIGONOMETRY IN EXTENDED HYPERBOLIC SPACE AND EXTENDED DE SITTER SPACE
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 Title & Authors
RIGONOMETRY IN EXTENDED HYPERBOLIC SPACE AND EXTENDED DE SITTER SPACE
Cho, Yun-Hi;
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 Abstract
We study the hyperbolic cosine and sine laws in the extended hyperbolic space which contains hyperbolic space as a subset and is an analytic continuation of the hyperbolic space. And we also study the spherical cosine and sine laws in the extended de Sitter space which contains de Sitter space S as a subset and is also an analytic continuation of de Sitter space. In fact, the extended hyperbolic space and extended de Sitter space are the same space only differ by -1 multiple in the metric. Hence these two extended spaces clearly show and apparently explain that why many corresponding formulas in hyperbolic and spherical space are very similar each other. From these extended trigonometry laws, we can give a coherent and geometrically simple explanation for the various relations between the lengths and angles of hyperbolic polygons, and relations on de Sitter polygons which lie on S, and tangent laws for various polyhedra.
 Keywords
hyperbolic space;volume;analytic continuation;
 Language
English
 Cited by
1.
GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE,;;

대한수학회지, 2013. vol.50. 6, pp.1223-1256 crossref(new window)
2.
AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA,;

대한수학회논문집, 2013. vol.28. 4, pp.799-807 crossref(new window)
1.
GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE, Journal of the Korean Mathematical Society, 2013, 50, 6, 1223  crossref(new windwow)
2.
On the area of a trihedral on a hyperbolic plane of positive curvature, Siberian Advances in Mathematics, 2015, 25, 2, 138  crossref(new windwow)
3.
Inequalities of trihedrals on a hyperbolic plane of positive curvature, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2017, 58, 4, 723  crossref(new windwow)
4.
AN ELEMENTARY PROOF OF SFORZA-SANTALÓ RELATION FOR SPHERICAL AND HYPERBOLIC POLYHEDRA, Communications of the Korean Mathematical Society, 2013, 28, 4, 799  crossref(new windwow)
5.
The analytic continuation of hyperbolic space, Geometriae Dedicata, 2012, 161, 1, 129  crossref(new windwow)
6.
Duality structures and discrete conformal variations of piecewise constant curvature surfaces, Advances in Mathematics, 2017, 320, 250  crossref(new windwow)
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