Some New Characterizations of Trivial Ricci–Bourguignon Solitons
A Ricci–Bourguignon soliton is a self-similar solution to the Ricci–Bourguignon flow equation, and a Ricci–Bourguignon soliton is called trivial if its potential field is zero or killing. Each trivial Ricci–Bourguignon soliton is an Einstein manifold. The main purpose of this paper is to discover ge...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/7917018 |
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| _version_ | 1832583863656775680 |
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| author | Hana Al-Sodais Nasser Bin Turki Sharief Deshmukh Bang-Yen Chen Hemangi Madhusudan Shah |
| author_facet | Hana Al-Sodais Nasser Bin Turki Sharief Deshmukh Bang-Yen Chen Hemangi Madhusudan Shah |
| author_sort | Hana Al-Sodais |
| collection | DOAJ |
| description | A Ricci–Bourguignon soliton is a self-similar solution to the Ricci–Bourguignon flow equation, and a Ricci–Bourguignon soliton is called trivial if its potential field is zero or killing. Each trivial Ricci–Bourguignon soliton is an Einstein manifold. The main purpose of this paper is to discover geometric conditions on compact Ricci–Bourguignon solitons for which the solitons are trivial. In Section 3, we establish three new characterizations for a compact connected Ricci–Bourguignon soliton to be trivial. In Section 4, we discover three conditions which assure that a compact gradient Ricci–Bourguignon soliton is trivial. Some applications of our results are also presented. |
| format | Article |
| id | doaj-art-b98d6b61a57d4f52972f0e5612de3846 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b98d6b61a57d4f52972f0e5612de38462025-01-28T05:00:03ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/7917018Some New Characterizations of Trivial Ricci–Bourguignon SolitonsHana Al-Sodais0Nasser Bin Turki1Sharief Deshmukh2Bang-Yen Chen3Hemangi Madhusudan Shah4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsHomi Bhabha National InstituteA Ricci–Bourguignon soliton is a self-similar solution to the Ricci–Bourguignon flow equation, and a Ricci–Bourguignon soliton is called trivial if its potential field is zero or killing. Each trivial Ricci–Bourguignon soliton is an Einstein manifold. The main purpose of this paper is to discover geometric conditions on compact Ricci–Bourguignon solitons for which the solitons are trivial. In Section 3, we establish three new characterizations for a compact connected Ricci–Bourguignon soliton to be trivial. In Section 4, we discover three conditions which assure that a compact gradient Ricci–Bourguignon soliton is trivial. Some applications of our results are also presented.http://dx.doi.org/10.1155/jom/7917018 |
| spellingShingle | Hana Al-Sodais Nasser Bin Turki Sharief Deshmukh Bang-Yen Chen Hemangi Madhusudan Shah Some New Characterizations of Trivial Ricci–Bourguignon Solitons Journal of Mathematics |
| title | Some New Characterizations of Trivial Ricci–Bourguignon Solitons |
| title_full | Some New Characterizations of Trivial Ricci–Bourguignon Solitons |
| title_fullStr | Some New Characterizations of Trivial Ricci–Bourguignon Solitons |
| title_full_unstemmed | Some New Characterizations of Trivial Ricci–Bourguignon Solitons |
| title_short | Some New Characterizations of Trivial Ricci–Bourguignon Solitons |
| title_sort | some new characterizations of trivial ricci bourguignon solitons |
| url | http://dx.doi.org/10.1155/jom/7917018 |
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