Open AccessSome Geometric Properties of a Non-Strict Eight Dimensional Walker Manifold
Author(s) -
Silas Longwap,
Gukat G. Bitrus,
C. Chibuisi
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i530367
Subject(s) - ricci curvature , mathematics , connection (principal bundle) , manifold (fluid mechanics) , combinatorics , function (biology) , pure mathematics , metric (unit) , closed manifold , curvature , invariant manifold , geometry , mechanical engineering , operations management , evolutionary biology , engineering , economics , biology
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.