Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation
The straight lines three-dimensional vector space realize the shortest distance for various metrics. This property is reformulated in terms of the inverse problem of the calculus of variations and closely related to the ultrahyperbolic equation with four independent variables. The interrelation is u...
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| Опубліковано в: : | Таврический вестник информатики и математики |
|---|---|
| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Кримський науковий центр НАН України і МОН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/18185 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation / V. Chrastinova // Таврический вестник информатики и математики. — 2010. — № 1. — С. 35-49. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862569578750541824 |
|---|---|
| author | Chrastinova, V. |
| author_facet | Chrastinova, V. |
| citation_txt | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation / V. Chrastinova // Таврический вестник информатики и математики. — 2010. — № 1. — С. 35-49. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Таврический вестник информатики и математики |
| description | The straight lines three-dimensional vector space realize the shortest distance for various metrics. This property is reformulated in terms of the inverse problem of the calculus of variations and closely related to the ultrahyperbolic equation with four independent variables. The interrelation is useful in both directions. For instans, polynomial solutions of the ultrahyperbolic equation provide all polynomial metrics with extremals the straight lines and conversely, a slight generalization of the Hilbert metrics leads to rather nontrivial (multi-valued of focusing) solutions of the ultrahyperbolic equation. In general, the article clarifies some well-known achievements concerning the 4th Hilbert Problem.
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| first_indexed | 2025-11-26T01:45:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-18185 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1729-3901 |
| language | English |
| last_indexed | 2025-11-26T01:45:38Z |
| publishDate | 2010 |
| publisher | Кримський науковий центр НАН України і МОН України |
| record_format | dspace |
| spelling | Chrastinova, V. 2011-03-18T12:41:38Z 2011-03-18T12:41:38Z 2010 Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation / V. Chrastinova // Таврический вестник информатики и математики. — 2010. — № 1. — С. 35-49. — Бібліогр.: 11 назв. — англ. 1729-3901 https://nasplib.isofts.kiev.ua/handle/123456789/18185 The straight lines three-dimensional vector space realize the shortest distance for various metrics. This property is reformulated in terms of the inverse problem of the calculus of variations and closely related to the ultrahyperbolic equation with four independent variables. The interrelation is useful in both directions. For instans, polynomial solutions of the ultrahyperbolic equation provide all polynomial metrics with extremals the straight lines and conversely, a slight generalization of the Hilbert metrics leads to rather nontrivial (multi-valued of focusing) solutions of the ultrahyperbolic equation. In general, the article clarifies some well-known achievements concerning the 4th Hilbert Problem. en Кримський науковий центр НАН України і МОН України Таврический вестник информатики и математики Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation Article published earlier |
| spellingShingle | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation Chrastinova, V. |
| title | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation |
| title_full | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation |
| title_fullStr | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation |
| title_full_unstemmed | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation |
| title_short | Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation |
| title_sort | straight lines in three-dimensional space and the ultrahyperbolic equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/18185 |
| work_keys_str_mv | AT chrastinovav straightlinesinthreedimensionalspaceandtheultrahyperbolicequation |