<i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds
The subject of the present paper is the investigation of a new type of solitons, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ri...
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3200 |
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| author | Arpan Sardar Mohammad Nazrul Islam Khan Uday Chand De |
| author_facet | Arpan Sardar Mohammad Nazrul Islam Khan Uday Chand De |
| author_sort | Arpan Sardar |
| collection | DOAJ |
| description | The subject of the present paper is the investigation of a new type of solitons, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ricci solitons in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-almost co-Kähler manifold (briefly, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula>), which generalizes the notion of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula> is obtained. Additionally, we classify the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ricci solitons in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula>s. Next, we investigate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula>s admitting gradient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ricci solitons. Finally, we construct two examples to illustrate our results. |
| first_indexed | 2024-03-10T03:38:25Z |
| format | Article |
| id | doaj.art-b422604b601e42cf94c47c63e5e3da46 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:38:25Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-b422604b601e42cf94c47c63e5e3da462023-11-23T09:25:39ZengMDPI AGMathematics2227-73902021-12-01924320010.3390/math9243200<i>η</i>-∗-Ricci Solitons and Almost co-Kähler ManifoldsArpan Sardar0Mohammad Nazrul Islam Khan1Uday Chand De2Department of Mathematics, University of Kalyani, Kalyani 741235, IndiaDepartment of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, IndiaThe subject of the present paper is the investigation of a new type of solitons, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ricci solitons in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-almost co-Kähler manifold (briefly, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula>), which generalizes the notion of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula> is obtained. Additionally, we classify the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ricci solitons in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula>s. Next, we investigate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mi>c</mi><mi>k</mi><mi>m</mi></mrow></semantics></math></inline-formula>s admitting gradient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-∗-Ricci solitons. Finally, we construct two examples to illustrate our results.https://www.mdpi.com/2227-7390/9/24/3200∗-Ricci tensor<i>η</i>-∗-Ricci solitonsgradient <i>η</i>-∗-Ricci solitonsalmost co-Kähler manifolds(<i>k</i>,<i>μ</i>)-almost co-Kähler manifolds |
| spellingShingle | Arpan Sardar Mohammad Nazrul Islam Khan Uday Chand De <i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds Mathematics ∗-Ricci tensor <i>η</i>-∗-Ricci solitons gradient <i>η</i>-∗-Ricci solitons almost co-Kähler manifolds (<i>k</i>,<i>μ</i>)-almost co-Kähler manifolds |
| title | <i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds |
| title_full | <i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds |
| title_fullStr | <i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds |
| title_full_unstemmed | <i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds |
| title_short | <i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds |
| title_sort | i η i ∗ ricci solitons and almost co kahler manifolds |
| topic | ∗-Ricci tensor <i>η</i>-∗-Ricci solitons gradient <i>η</i>-∗-Ricci solitons almost co-Kähler manifolds (<i>k</i>,<i>μ</i>)-almost co-Kähler manifolds |
| url | https://www.mdpi.com/2227-7390/9/24/3200 |
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