Geometric classification of totally umbilical quasi-hemislant submanifolds
UDC 514.76, 514.77 We study the geometric characteristics and classification of totally umbilical quasi-hemislant submanifolds in almost product Riemannian manifolds. We focus on three primary distributions: the slant distribution $D^\theta,$ the totally real distribution $D^\bot,$ and the invariant...
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| Дата: | 2026 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9095 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1871646550641344512 |
|---|---|
| author | Fatima, Tanveer Deshmukh, Sharief Fatima, Tanveer Deshmukh, Sharief |
| author_facet | Fatima, Tanveer Deshmukh, Sharief Fatima, Tanveer Deshmukh, Sharief |
| author_institution_txt_mv | [
{
"author": "Tanveer Fatima",
"institution": "Department of Mathematics and Statistics, \t\t College of Sciences in Yanbu, Taibah University, Yanbu Covernorate, Saudi Arabia"
},
{
"author": "Sharief Deshmukh",
"institution": "Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia"
}
] |
| author_sort | Fatima, Tanveer |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:13Z |
| description | UDC 514.76, 514.77
We study the geometric characteristics and classification of totally umbilical quasi-hemislant submanifolds in almost product Riemannian manifolds. We focus on three primary distributions: the slant distribution $D^\theta,$ the totally real distribution $D^\bot,$ and the invariant distribution $D,$ providing a detailed analysis of their integrability conditions and conditions of being totally geodesic. Through these investigations, we found that these submanifolds can be categorized as totally geodesic, CR submanifolds, or exhibits other interesting geometric properties, such as being extrinsic spheres or proper semislant submanifolds depending on specific geometric conditions. We establish necessary and sufficient conditions for each classification and describe possible structural configurations of these submanifolds. Our results contribute to a broader comprehension of quasi-hemislant submanifolds in differential geometry by providing new classifications and geometric perspective in almost product Riemannian structures. |
| doi_str_mv | 10.3842/umzh.v78i7-8.9095 |
| first_indexed | 2026-07-25T01:00:44Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9095 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:00:44Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-90952026-07-24T15:24:13Z Geometric classification of totally umbilical quasi-hemislant submanifolds Geometric classification of totally umbilical quasi-hemislant submanifolds Fatima, Tanveer Deshmukh, Sharief Fatima, Tanveer Deshmukh, Sharief Quasi hemi-slant submanifolds Almost product Riemannian manifolds Totally umbilical submanifolds Riemannian submanifold 53C43 53D10 UDC 514.76, 514.77 We study the geometric characteristics and classification of totally umbilical quasi-hemislant submanifolds in almost product Riemannian manifolds. We focus on three primary distributions: the slant distribution $D^\theta,$ the totally real distribution $D^\bot,$ and the invariant distribution $D,$ providing a detailed analysis of their integrability conditions and conditions of being totally geodesic. Through these investigations, we found that these submanifolds can be categorized as totally geodesic, CR submanifolds, or exhibits other interesting geometric properties, such as being extrinsic spheres or proper semislant submanifolds depending on specific geometric conditions. We establish necessary and sufficient conditions for each classification and describe possible structural configurations of these submanifolds. Our results contribute to a broader comprehension of quasi-hemislant submanifolds in differential geometry by providing new classifications and geometric perspective in almost product Riemannian structures. УДК 514.76, 514.77 Геометрична класифікація цілком омбілічних квазінапівпохилих підмноговидів Досліджено геометричні характеристики та класифікацію цілком омбілічних квазінапівпохилих підмноговидів у майже добуткових ріманових многовидах. Основну увагу зосереджено на трьох базових розподілах: похилому розподілі $D^\theta,$ цілком дійсному розподілі $D^\bot$ та інваріантному розподілі $D,$ для яких детально проаналізовано умови інтегровності та повної геодезичності. Встановлено, що за певних геометричних умов такі підмноговиди можуть бути цілком геодезичними, CR-підмноговидами або мати інші цікаві геометричні властивості, зокрема бути зовнішніми сферами чи власними напівпохилими підмноговидами. Отримано необхідні та достатні умови для кожного з цих класів та описано можливі структурні конфігурації зазначених підмноговидів. Результати роботи розширюють розуміння квазінапівпохилих підмноговидів у диференціальній геометрії та дають новий погляд на їхню класифікацію в майже добуткових ріманових структурах. Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9095 10.3842/umzh.v78i7-8.9095 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 601–602 Український математичний журнал; Том 78 № 7-8 (2026); 601–602 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9095/10684 Copyright (c) 2026 Tanveer Fatima, Sharief Deshmukh |
| spellingShingle | Fatima, Tanveer Deshmukh, Sharief Fatima, Tanveer Deshmukh, Sharief Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title | Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title_alt | Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title_full | Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title_fullStr | Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title_full_unstemmed | Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title_short | Geometric classification of totally umbilical quasi-hemislant submanifolds |
| title_sort | geometric classification of totally umbilical quasi-hemislant submanifolds |
| topic_facet | Quasi hemi-slant submanifolds Almost product Riemannian manifolds Totally umbilical submanifolds Riemannian submanifold 53C43 53D10 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9095 |
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