SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER METRIC ON A EIGHT-DIMENSIONAL MANIFOLDS
SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER...
A pseudo-Riemannian manifold which admits a field of parallel
null r-planes, with r ≤ n 2 is a Walker n-manifold. A.G. Walker in  investi-
gated the canonical forms of the metrics and came out with some interesting re-
sults. 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
consider a perticular eight-dimensional Walker manifold, derive and investigate
some geometric properties of the curvature tensors of the Manifold. We give
some theorems for the metric to be Einstein and Locally Conformally Flat.
How to Cite
Longwap, S., & SALAM DIALLO, A. (2022). SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER METRIC ON A EIGHT-DIMENSIONAL MANIFOLDS: SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER. Journal of the Nigerian Mathematical Society, 41(3), 223–234. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/873
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