Characterizations of Trivial Ricci Solitons
Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a ch...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/9826570 |
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| _version_ | 1832559243429937152 |
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| author | Sharief Deshmukh Nasser Bin Turki Hana Alsodais |
| author_facet | Sharief Deshmukh Nasser Bin Turki Hana Alsodais |
| author_sort | Sharief Deshmukh |
| collection | DOAJ |
| description | Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a characterization of a trivial Ricci soliton. Then, it is shown that the potential field having geodesic flow and length of potential field satisfying certain inequality gives another characterization of a trivial Ricci soliton. Finally, we show that the potential field of constant length satisfying an inequality gives a characterization of a trivial Ricci soliton. |
| format | Article |
| id | doaj-art-d0f4a4d187044c74b5056d6e319d9715 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d0f4a4d187044c74b5056d6e319d97152025-02-03T01:30:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/98265709826570Characterizations of Trivial Ricci SolitonsSharief Deshmukh0Nasser Bin Turki1Hana Alsodais2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFinding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a characterization of a trivial Ricci soliton. Then, it is shown that the potential field having geodesic flow and length of potential field satisfying certain inequality gives another characterization of a trivial Ricci soliton. Finally, we show that the potential field of constant length satisfying an inequality gives a characterization of a trivial Ricci soliton.http://dx.doi.org/10.1155/2020/9826570 |
| spellingShingle | Sharief Deshmukh Nasser Bin Turki Hana Alsodais Characterizations of Trivial Ricci Solitons Advances in Mathematical Physics |
| title | Characterizations of Trivial Ricci Solitons |
| title_full | Characterizations of Trivial Ricci Solitons |
| title_fullStr | Characterizations of Trivial Ricci Solitons |
| title_full_unstemmed | Characterizations of Trivial Ricci Solitons |
| title_short | Characterizations of Trivial Ricci Solitons |
| title_sort | characterizations of trivial ricci solitons |
| url | http://dx.doi.org/10.1155/2020/9826570 |
| work_keys_str_mv | AT shariefdeshmukh characterizationsoftrivialriccisolitons AT nasserbinturki characterizationsoftrivialriccisolitons AT hanaalsodais characterizationsoftrivialriccisolitons |