Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons
The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics><...
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| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/140 |
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| author | Halil İbrahim Yoldaş Abdul Haseeb Fatemah Mofarreh |
| author_facet | Halil İbrahim Yoldaş Abdul Haseeb Fatemah Mofarreh |
| author_sort | Halil İbrahim Yoldaş |
| collection | DOAJ |
| description | The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci solitons. First we find some necessary conditions for such a manifold to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Einstein. Then, we study the notion of 🟉-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. |
| first_indexed | 2024-03-11T09:09:53Z |
| format | Article |
| id | doaj.art-565831317b18435abf565d9b224a61df |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:09:53Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-565831317b18435abf565d9b224a61df2023-11-16T19:05:49ZengMDPI AGAxioms2075-16802023-01-0112214010.3390/axioms12020140Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci SolitonsHalil İbrahim Yoldaş0Abdul Haseeb1Fatemah Mofarreh2Department of Management Information Systems, Adana Alparslan Türkeş Science and Technology University, 01250 Adana, TurkeyDepartment of Mathematics, College of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi ArabiaMathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 13415, Riyadh 11546, Saudi ArabiaThe present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci solitons. First we find some necessary conditions for such a manifold to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Einstein. Then, we study the notion of 🟉-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results.https://www.mdpi.com/2075-1680/12/2/140?-Ricci tensor?-<i>η</i>-Ricci solitonKenmotsu manifoldsprojective curvature tensorconcircular curvature tensorℳ-projective curvature tensor |
| spellingShingle | Halil İbrahim Yoldaş Abdul Haseeb Fatemah Mofarreh Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons Axioms ?-Ricci tensor ?-<i>η</i>-Ricci soliton Kenmotsu manifolds projective curvature tensor concircular curvature tensor ℳ-projective curvature tensor |
| title | Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons |
| title_full | Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons |
| title_fullStr | Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons |
| title_full_unstemmed | Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons |
| title_short | Certain Curvature Conditions on Kenmotsu Manifolds and 🟉-<i>η</i>-Ricci Solitons |
| title_sort | certain curvature conditions on kenmotsu manifolds and 🟉 i η i ricci solitons |
| topic | ?-Ricci tensor ?-<i>η</i>-Ricci soliton Kenmotsu manifolds projective curvature tensor concircular curvature tensor ℳ-projective curvature tensor |
| url | https://www.mdpi.com/2075-1680/12/2/140 |
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