On the number of critical submanifolds of a function on a manifold
We consider differentiable functions on a manifold such that the set of their critical points is a disconnected union of smooth submanifolds. A topological characteristic of the manifold is introduced; in terms of this characteristic, we estimate the least possible number of critical submanifolds of...
Gespeichert in:
| Datum: | 1993 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1993
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5979 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512200812134400 |
|---|---|
| author | Bondar', O. P. Бондарь, О. П. Бондарь, О. П. |
| author_facet | Bondar', O. P. Бондарь, О. П. Бондарь, О. П. |
| author_sort | Bondar', O. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:22:20Z |
| description | We consider differentiable functions on a manifold such that the set of their critical points is a disconnected union of smooth submanifolds. A topological characteristic of the manifold is introduced; in terms of this characteristic, we estimate the least possible number of critical submanifolds of these functions. |
| first_indexed | 2026-03-24T03:25:01Z |
| format | Article |
| fulltext |
0116
0117
0118
0119
|
| id | umjimathkievua-article-5979 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:25:01Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3a/a1c0bcbcfd66b4cd38723a17db65c03a.pdf |
| spelling | umjimathkievua-article-59792020-03-19T09:22:20Z On the number of critical submanifolds of a function on a manifold О числе критических подмногообразий функции на многообразии Bondar', O. P. Бондарь, О. П. Бондарь, О. П. We consider differentiable functions on a manifold such that the set of their critical points is a disconnected union of smooth submanifolds. A topological characteristic of the manifold is introduced; in terms of this characteristic, we estimate the least possible number of critical submanifolds of these functions. Розглядаються диференційовні функції на многовиді, у котрих множина критичних точок є незв’язним об’єднанням гладких підмноговидів. Введено топологічну характеристику многовиду, в термінах якої наводиться оцінка найменшого можливого числа критичних підмноговидів та ких функцій. Institute of Mathematics, NAS of Ukraine 1993-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5979 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 12 (1993); 1702–1705 Український математичний журнал; Том 45 № 12 (1993); 1702–1705 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5979/8641 https://umj.imath.kiev.ua/index.php/umj/article/view/5979/8642 Copyright (c) 1993 Bondar' O. P. |
| spellingShingle | Bondar', O. P. Бондарь, О. П. Бондарь, О. П. On the number of critical submanifolds of a function on a manifold |
| title | On the number of critical submanifolds of a function on a manifold |
| title_alt | О числе критических подмногообразий функции на многообразии |
| title_full | On the number of critical submanifolds of a function on a manifold |
| title_fullStr | On the number of critical submanifolds of a function on a manifold |
| title_full_unstemmed | On the number of critical submanifolds of a function on a manifold |
| title_short | On the number of critical submanifolds of a function on a manifold |
| title_sort | on the number of critical submanifolds of a function on a manifold |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5979 |
| work_keys_str_mv | AT bondar039op onthenumberofcriticalsubmanifoldsofafunctiononamanifold AT bondarʹop onthenumberofcriticalsubmanifoldsofafunctiononamanifold AT bondarʹop onthenumberofcriticalsubmanifoldsofafunctiononamanifold AT bondar039op očislekritičeskihpodmnogoobrazijfunkciinamnogoobrazii AT bondarʹop očislekritičeskihpodmnogoobrazijfunkciinamnogoobrazii AT bondarʹop očislekritičeskihpodmnogoobrazijfunkciinamnogoobrazii |