KFU. Card publication. Metric Characteristics of Hyperbolic Polygons and Polyhedra.

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FEDERAL UNIVERSITY

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METRIC CHARACTERISTICS OF HYPERBOLIC POLYGONS AND POLYHEDRA.

Form of presentation

Articles in international journals and collections

Year of publication

2022

Язык

русский

Authors, employees of KFU

Kostina Natalya Nikolaevna, author

Other authors

Kostina Evgeniya Andreevna, author

Bibliographic description in the original language

Kostina, N.N. Metric Characteristics of Hyperbolic Polygons and Polyhedra / Kostina, E.A., Kostina, N.N. // J Math Sci 263, 379–386 (2022). https://doi.org/10.1007/s10958-022-05934-5

Annotation

In this paper, we consider some properties of hyperbolic polyhedra, both common with Euclidean and specific. Asymptotic behavior of metric characteristics of polyhedra in the n-dimensional hyperbolic space is examined in the cases where parameters of the polyhedra change and the dimension of the space unboundedly increases; in particular, the radius of the inscribed sphere of a polyhedron is estimated and its asymptotic behavior is obtained. In connection with this, the problem of estimating the minimal number of faces of the described polyhedron in the n-dimensional hyperbolic space depending on the radius of the inscribed sphere is posed. We also consider some properties of hyperbolic polygons that belong to both absolute geometry or only to hyperbolic geometry.

Keywords

Lobachevsky space, hyperbolic trigonometry, polygon, polyhedron, sphere, simplex

The name of the journal

Journal of Mathematical Sciences

URL

https://link.springer.com/article/10.1007/s10958-022-05934-5

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=268689&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Kostina Natalya Nikolaevna	ru_RU
dc.contributor.author	Kostina Evgeniya Andreevna	ru_RU
dc.date.accessioned	2022-01-01T00:00:00Z	ru_RU
dc.date.available	2022-01-01T00:00:00Z	ru_RU
dc.date.issued	2022	ru_RU
dc.identifier.citation	Kostina, N.N. Metric Characteristics of Hyperbolic Polygons and Polyhedra / Kostina, E.A., Kostina, N.N. // J Math Sci 263, 379–386 (2022). https://doi.org/10.1007/s10958-022-05934-5	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=268689&p_lang=2	ru_RU
dc.description.abstract	Journal of Mathematical Sciences	ru_RU
dc.description.abstract	In this paper, we consider some properties of hyperbolic polyhedra, both common with Euclidean and specific. Asymptotic behavior of metric characteristics of polyhedra in the n-dimensional hyperbolic space is examined in the cases where parameters of the polyhedra change and the dimension of the space unboundedly increases; in particular, the radius of the inscribed sphere of a polyhedron is estimated and its asymptotic behavior is obtained. In connection with this, the problem of estimating the minimal number of faces of the described polyhedron in the n-dimensional hyperbolic space depending on the radius of the inscribed sphere is posed. We also consider some properties of hyperbolic polygons that belong to both absolute geometry or only to hyperbolic geometry.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Lobachevsky space	ru_RU
dc.subject	hyperbolic trigonometry	ru_RU
dc.subject	polygon	ru_RU
dc.subject	polyhedron	ru_RU
dc.subject	sphere	ru_RU
dc.subject	simplex	ru_RU
dc.title	Metric Characteristics of Hyperbolic Polygons and Polyhedra.	ru_RU
dc.type	Articles in international journals and collections	ru_RU