WALKER OSSERMAN METRIC OF SIGNATURE (3,3,)

摘要

A Walker m-manifold is a pseudo-Riemannian manifold, which admits a field of parallel null r-planes, with r ≤m/2. The Riemann extension is an important method to produce Walker metric on the cotangent bundle T ? M of any affine manifold (M,?). In this paper, we investigate the torsion-free affine manifold (M,?) and their Riemann extension (T ? M, ˉ g) as concerns heredity of the Osserman condition.