Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds
We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvatur...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/6673918 |
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| _version_ | 1832550524200681472 |
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| author | Ntokozo Sibonelo Khuzwayo Fortuné Massamba |
| author_facet | Ntokozo Sibonelo Khuzwayo Fortuné Massamba |
| author_sort | Ntokozo Sibonelo Khuzwayo |
| collection | DOAJ |
| description | We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves. |
| format | Article |
| id | doaj-art-e2d092e9c40645b1b0a3cec7f08f3d59 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e2d092e9c40645b1b0a3cec7f08f3d592025-02-03T06:06:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252021-01-01202110.1155/2021/66739186673918Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler ManifoldsNtokozo Sibonelo Khuzwayo0Fortuné Massamba1School of Mathematics, Statistics and Computer Science, University of Kwazulu-Natal, Private Bag X01, Scottsville 3209, South AfricaSchool of Mathematics, Statistics and Computer Science, University of Kwazulu-Natal, Private Bag X01, Scottsville 3209, South AfricaWe investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.http://dx.doi.org/10.1155/2021/6673918 |
| spellingShingle | Ntokozo Sibonelo Khuzwayo Fortuné Massamba Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds International Journal of Mathematics and Mathematical Sciences |
| title | Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds |
| title_full | Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds |
| title_fullStr | Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds |
| title_full_unstemmed | Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds |
| title_short | Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds |
| title_sort | some properties of curvature tensors and foliations of locally conformal almost kahler manifolds |
| url | http://dx.doi.org/10.1155/2021/6673918 |
| work_keys_str_mv | AT ntokozosibonelokhuzwayo somepropertiesofcurvaturetensorsandfoliationsoflocallyconformalalmostkahlermanifolds AT fortunemassamba somepropertiesofcurvaturetensorsandfoliationsoflocallyconformalalmostkahlermanifolds |