Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields
In this paper, we give some classifications of the <i>k</i>-Yamabe solitons on the hypersurfaces of the Euclidean spaces from the vector field point of view. In several results on <i>k</i>-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds,...
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MDPI AG
2021-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/2/222 |
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| author | Akram Ali Fatemah Mofarreh Pişcoran Laurian-Ioan Nadia Alluhaibi |
| author_facet | Akram Ali Fatemah Mofarreh Pişcoran Laurian-Ioan Nadia Alluhaibi |
| author_sort | Akram Ali |
| collection | DOAJ |
| description | In this paper, we give some classifications of the <i>k</i>-Yamabe solitons on the hypersurfaces of the Euclidean spaces from the vector field point of view. In several results on <i>k</i>-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds, is proved that a <i>k</i>-Yamabe soliton <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msup><mi>M</mi><mi>n</mi></msup><mo>,</mo><mi>g</mi><mo>,</mo><msup><mi>v</mi><mi>T</mi></msup><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></semantics></math></inline-formula> on a hypersurface in the Euclidean space <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> is contained either in a hypersphere or a hyperplane. We provide an example to support this study and all of the results in this paper can be implemented to Yamabe solitons for <i>k</i>-curvature with <inline-formula><math display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T03:20:17Z |
| format | Article |
| id | doaj.art-57fbf0805794481f9006d99085f4afac |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:20:17Z |
| publishDate | 2021-01-01 |
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| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-57fbf0805794481f9006d99085f4afac2023-12-03T15:11:59ZengMDPI AGSymmetry2073-89942021-01-0113222210.3390/sym13020222Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector FieldsAkram Ali0Fatemah Mofarreh1Pişcoran Laurian-Ioan2Nadia Alluhaibi3Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi ArabiaMathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi ArabiaDepartment of Mathematics and Computer Science Victoriei 76, North University Center of Baia Mare Technical University of Cluj Napoca, 430122 Baia Mare, RomaniaDepartment of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah 21911, Saudi ArabiaIn this paper, we give some classifications of the <i>k</i>-Yamabe solitons on the hypersurfaces of the Euclidean spaces from the vector field point of view. In several results on <i>k</i>-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds, is proved that a <i>k</i>-Yamabe soliton <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msup><mi>M</mi><mi>n</mi></msup><mo>,</mo><mi>g</mi><mo>,</mo><msup><mi>v</mi><mi>T</mi></msup><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></semantics></math></inline-formula> on a hypersurface in the Euclidean space <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> is contained either in a hypersphere or a hyperplane. We provide an example to support this study and all of the results in this paper can be implemented to Yamabe solitons for <i>k</i>-curvature with <inline-formula><math display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2073-8994/13/2/222concurrent vector fieldsk-Yamabe solitonshypersurfaceEuclidean spaces |
| spellingShingle | Akram Ali Fatemah Mofarreh Pişcoran Laurian-Ioan Nadia Alluhaibi Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields Symmetry concurrent vector fields k-Yamabe solitons hypersurface Euclidean spaces |
| title | Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields |
| title_full | Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields |
| title_fullStr | Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields |
| title_full_unstemmed | Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields |
| title_short | Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields |
| title_sort | geometry of em k em yamabe solitons on euclidean spaces and its applications to concurrent vector fields |
| topic | concurrent vector fields k-Yamabe solitons hypersurface Euclidean spaces |
| url | https://www.mdpi.com/2073-8994/13/2/222 |
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