Critical point equation on $K$-contact generalized Sasakian space form
UDC 514.7 We investigate the critical-point equation within the framework of $K$-contact generalized Sasakian space forms. It is demonstrated that a complete $K$-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere $S^{2n+1...
Saved in:
| Date: | 2026 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9409 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865795298824028160 |
|---|---|
| author | Pavithra, R. C. Nagaraja, H. G. Pavithra, R. C. Nagaraja, H. G. |
| author_facet | Pavithra, R. C. Nagaraja, H. G. Pavithra, R. C. Nagaraja, H. G. |
| author_institution_txt_mv | [
{
"author": "R. C. Pavithra",
"institution": "Department of Mathematics, Bangalore University, Jnanabharathi, Bengalure, Karnataka, India"
},
{
"author": "H. G. Nagaraja",
"institution": "Department of Mathematics, Bangalore University, Jnanabharathi, Bengalure, Karnataka, India"
}
] |
| author_sort | Pavithra, R. C. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-04-23T13:14:25Z |
| description | UDC 514.7
We investigate the critical-point equation within the framework of $K$-contact generalized Sasakian space forms. It is demonstrated that a complete $K$-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere $S^{2n+1}$. In addition, we show that if this space form satisfies the Euler–Lagrange equation corresponding to the total scalar curvature functional, then it is Einstein and also satisfies the Fischer–Marsden equation. An illustrative example is provided to support and validate our theoretical findings. |
| doi_str_mv | 10.3842/umzh.v78i3-4.9409 |
| first_indexed | 2026-03-29T01:00:33Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9409 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-24T01:00:26Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-94092026-04-23T13:14:25Z Critical point equation on $K$-contact generalized Sasakian space form Critical point equation on $K$-contact generalized Sasakian space form Pavithra, R. C. Nagaraja, H. G. Pavithra, R. C. Nagaraja, H. G. $K$-contact generalized Sasakian space form, Miao-Tam equation, Euler-Lagranges equation, Fischer-Marsden equation, Einstein manifold. 53C25, 53C15, 53D15. UDC 514.7 We investigate the critical-point equation within the framework of $K$-contact generalized Sasakian space forms. It is demonstrated that a complete $K$-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere $S^{2n+1}$. In addition, we show that if this space form satisfies the Euler–Lagrange equation corresponding to the total scalar curvature functional, then it is Einstein and also satisfies the Fischer–Marsden equation. An illustrative example is provided to support and validate our theoretical findings. УДК 514.7 Рівняння критичної точки на $K$-контактній узагальненій формі простору Сасакіана Розглянуто рівняння критичної точки в рамках $K$-контактних узагальнених просторових форм Сасакіана. Показано, що повна $K$-контактна узагальнена просторова форма Сасакіана, яка задовольняє рівняння Мяо–Тама, обов'язково є ейнштейнівською та ізометричною до одиничної сфери $S^{2n+1}$. Крім того, показано, що якщо така просторова форма задовольняє рівняння Ейлера–Лагранжа, яке відповідає функціоналу загальної скалярної кривини, то вона є ейнштейнівською і також задовольняє рівняння Фішера–Марсдена. Наведено наочний приклад для підтвердження та обґрунтування одержаних теоретичних висновків. Institute of Mathematics, NAS of Ukraine 2026-04-03 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9409 10.3842/umzh.v78i3-4.9409 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 3-4 (2026); 212 Український математичний журнал; Том 78 № 3-4 (2026); 212 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9409/10637 Copyright (c) 2026 R. C. Pavithra, H. G. Nagaraja |
| spellingShingle | Pavithra, R. C. Nagaraja, H. G. Pavithra, R. C. Nagaraja, H. G. Critical point equation on $K$-contact generalized Sasakian space form |
| title | Critical point equation on $K$-contact generalized Sasakian space form |
| title_alt | Critical point equation on $K$-contact generalized Sasakian space form |
| title_full | Critical point equation on $K$-contact generalized Sasakian space form |
| title_fullStr | Critical point equation on $K$-contact generalized Sasakian space form |
| title_full_unstemmed | Critical point equation on $K$-contact generalized Sasakian space form |
| title_short | Critical point equation on $K$-contact generalized Sasakian space form |
| title_sort | critical point equation on $k$-contact generalized sasakian space form |
| topic_facet | $K$-contact generalized Sasakian space form, Miao-Tam equation, Euler-Lagranges equation, Fischer-Marsden equation, Einstein manifold. 53C25, 53C15, 53D15. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9409 |
| work_keys_str_mv | AT pavithrarc criticalpointequationonkcontactgeneralizedsasakianspaceform AT nagarajahg criticalpointequationonkcontactgeneralizedsasakianspaceform AT pavithrarc criticalpointequationonkcontactgeneralizedsasakianspaceform AT nagarajahg criticalpointequationonkcontactgeneralizedsasakianspaceform |