Quarter-Symmetric Metric Connection on a Cosymplectic Manifold
We study the quarter-symmetric metric <i>A</i>-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric <i>A</i>-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifol...
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| Format: | Article |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2209 |
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| author | Miroslav D. Maksimović Milan Lj. Zlatanović |
| author_facet | Miroslav D. Maksimović Milan Lj. Zlatanović |
| author_sort | Miroslav D. Maksimović |
| collection | DOAJ |
| description | We study the quarter-symmetric metric <i>A</i>-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric <i>A</i>-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Einstein cosymplectic manifolds of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-th kind and prove that they coincide with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Einstein cosymplectic manifold. |
| first_indexed | 2024-03-11T04:11:45Z |
| format | Article |
| id | doaj.art-02ab7e3bdbf94f24baceb7f60098515d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:11:45Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-02ab7e3bdbf94f24baceb7f60098515d2023-11-17T23:21:25ZengMDPI AGMathematics2227-73902023-05-01119220910.3390/math11092209Quarter-Symmetric Metric Connection on a Cosymplectic ManifoldMiroslav D. Maksimović0Milan Lj. Zlatanović1Department of Mathematics, Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaDepartment of Mathematics, Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, SerbiaWe study the quarter-symmetric metric <i>A</i>-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric <i>A</i>-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Einstein cosymplectic manifolds of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-th kind and prove that they coincide with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Einstein cosymplectic manifold.https://www.mdpi.com/2227-7390/11/9/2209almost-contact manifoldcosymplectic manifoldco-Kähler manifoldquarter-symmetric connection<i>η</i>-Einstein manifold |
| spellingShingle | Miroslav D. Maksimović Milan Lj. Zlatanović Quarter-Symmetric Metric Connection on a Cosymplectic Manifold Mathematics almost-contact manifold cosymplectic manifold co-Kähler manifold quarter-symmetric connection <i>η</i>-Einstein manifold |
| title | Quarter-Symmetric Metric Connection on a Cosymplectic Manifold |
| title_full | Quarter-Symmetric Metric Connection on a Cosymplectic Manifold |
| title_fullStr | Quarter-Symmetric Metric Connection on a Cosymplectic Manifold |
| title_full_unstemmed | Quarter-Symmetric Metric Connection on a Cosymplectic Manifold |
| title_short | Quarter-Symmetric Metric Connection on a Cosymplectic Manifold |
| title_sort | quarter symmetric metric connection on a cosymplectic manifold |
| topic | almost-contact manifold cosymplectic manifold co-Kähler manifold quarter-symmetric connection <i>η</i>-Einstein manifold |
| url | https://www.mdpi.com/2227-7390/11/9/2209 |
| work_keys_str_mv | AT miroslavdmaksimovic quartersymmetricmetricconnectiononacosymplecticmanifold AT milanljzlatanovic quartersymmetricmetricconnectiononacosymplecticmanifold |