Eight-Dimensional Walker Locally Symmetric Manifolds

Abstract

A pseudo-Riemannian manifold which admits a field of parallel null $r$-planes, with $r\leq \frac{m}{2}$ is a Walker $m$-manifold. The even-dimensional Walker manifolds $(m=2r)$ with fields of parallel null planes of half dimension have some special interest. The main purpose of the present paper is to study a specifc Walker metric on a $8$-dimensional manifold and to give a theorem for the metric to be locally symmetric.

Keywords

• Locally symmetric space
• Walker manifold.
• Pseudo-Riemannin

References

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