A Walker n-manifold is a pseudo-Riemannian manifold which admits a field of parallel null r-planes, with r ≤ n 2 . The canonical forms of the metrics were investigated by A. G. Walker [12]. 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 Kähler structure are given.
@article{7120,
title = {ALMOST K\"AHLER ON EIGHT-DIMENSIONAL WALKER MANIFOLDS},
journal = {Novi Sad Journal of Mathematics},
volume = {48},
year = {2018},
language = {EN},
url = {http://dml.mathdoc.fr/item/7120}
}
DIALLO, Abdoul Salam. ALMOST KÄHLER ON EIGHT-DIMENSIONAL WALKER MANIFOLDS. Novi Sad Journal of Mathematics, Tome 48 (2018) . http://gdmltest.u-ga.fr/item/7120/