Geodesic
Almost Kähler eight-dimensional Walker manifold
Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1.

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A Walker $n$-manifold is a pseudo-Riemannian manifold which admits a field of parallel null $r$-planes, with $r\leq \frac{n}{2}$. The canonical forms of the metrics were investigated by A. G. Walker \cite{walker}. Of special interest are the even-dimensional Walker manifolds $(n=2m)$ with fields of parallel null planes of half dimension $(r=m)$. In this paper, we investigate geometric properties of some curvature tensors of an eight-dimensional Walker manifold. Theorems for the metric to be Einstein, locally conformally flat and for the Walker eight-manifold to admit a K\"ahler structure are given.
Publié le :
DOI : 10.30755/NSJOM.07120
Classification : 53B30, 53B35
Keywords: Almost Kähler structure, Einstein manifold, Goldberg conjecture, Walker metrics 
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     author = {Abdoul Salam Diallo and Silas Longwap and Fortun\'e Massamba},
     title = {Almost {K\"ahler} eight-dimensional {Walker} manifold},
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     pages = {129 - 141},
     publisher = {mathdoc},
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     year = {2018},
     doi = {10.30755/NSJOM.07120},
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Abdoul Salam Diallo; Silas Longwap; Fortuné Massamba. Almost Kähler eight-dimensional Walker manifold. Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1. doi : 10.30755/NSJOM.07120. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.07120/

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