Some Geometric Properties of a Non-Strict Eight Dimensional Walker Manifold
Silas Longwap *
Department of Mathematics, Faculty of Natural Sciences, University of Jos, P.M.B. 2084, Plateau State, Nigeria.
Gukat G. Bitrus
Department of Mathematics and Computer Science, Federal University of Kashere, P.M.B. 0182, Gombe State, Nigeria.
Chibuisi Chigozie
Department of Insurance, University of Jos, P.M.B. 2084, Plateau State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
An 8 dimensional Walker manifold (M; g) is a strict walker manifold if we can choose a coordinate system fx1; x2; x3; x4; x5; x6; x7; x8g on (M,g) such that any function f on the manfold (M,g), f(x1; x2; x3; x4; x5; x6; x7; x8) = f(x5; x6; x7; x8): In this work, we dene a Non-strict eight dimensional walker manifold as the one that we can choose the coordinate system such that for any f in (M; g); f(x1; x2; x3; x4; x5; x6; x7; x8) = f(x1; x2; x3; x4): We derive cononical form of the Levi-Civita connection, curvature operator, (0; 4)-curvature tansor, the Ricci tensor, Weyl tensorand study some of the properties associated with the class of Non-strict 8 dimensionalWalker manifold. We investigate the Einstein property and establish a theorem for the metric to be locally conformally at.
Keywords: Pseudo-Riemannian manifold, eight dimensional walker manifold, non-strict walker manifold.