On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold
We study the possibility of constructing locally gradient and arbitrary vector fields with a given set of singular points on a two-dimensional closed oriented manifold. The sum of the indices of the vector field at these points is equal to the Euler characteristic of the manifold.
Збережено в:
| Дата: | 1993 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1993
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5980 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512202292723712 |
|---|---|
| author | Girik, E. A. Гирик, Е. А. Гирик, Е. А. |
| author_facet | Girik, E. A. Гирик, Е. А. Гирик, Е. А. |
| author_sort | Girik, E. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:22:20Z |
| description | We study the possibility of constructing locally gradient and arbitrary vector fields with a given set of singular points on a two-dimensional closed oriented manifold. The sum of the indices of the vector field at these points is equal to the Euler characteristic of the manifold. |
| first_indexed | 2026-03-24T03:25:02Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5980 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:25:02Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/40/e553355c023dc9f1a6114a2ebd8dd340.pdf |
| spelling | umjimathkievua-article-59802020-03-19T09:22:20Z On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold О существовании на двумерном замкнутом ориентируемом многообразии векторных полей с заданным набором особых точек Girik, E. A. Гирик, Е. А. Гирик, Е. А. We study the possibility of constructing locally gradient and arbitrary vector fields with a given set of singular points on a two-dimensional closed oriented manifold. The sum of the indices of the vector field at these points is equal to the Euler characteristic of the manifold. Досліджується можливість побудови на двовимірному замкненому орієнтованому многовиді локально ірадієнтних та довільних векторних полів з заданим набором особливих точок, сума індексів векторного поля в яких дорівнює ейлеровій характеристиці многовиду. Institute of Mathematics, NAS of Ukraine 1993-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5980 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 12 (1993); 1706–1709 Український математичний журнал; Том 45 № 12 (1993); 1706–1709 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5980/8643 https://umj.imath.kiev.ua/index.php/umj/article/view/5980/8644 Copyright (c) 1993 Girik E. A. |
| spellingShingle | Girik, E. A. Гирик, Е. А. Гирик, Е. А. On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| title | On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| title_alt | О существовании на двумерном замкнутом ориентируемом многообразии векторных полей с заданным набором особых точек |
| title_full | On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| title_fullStr | On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| title_full_unstemmed | On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| title_short | On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| title_sort | on the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5980 |
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