Eight-Dimensional Walker Locally Symmetric Manifolds

Authors : Silas Longwap, Abdoul Salam Diallo

Pages : 1-4

View : 80 | Download : 69

Publication Date : 2024-04-30

Article Type : Research Paper

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