Abstract
A Walker m-manifold is a pseudo-Riemannian manifold, which admits a field of parallel null r-planes, with \(r{\leqslant } \frac {m}{2}\). 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 \((T^* M,\bar {g})\) as concerns heredity of the Osserman condition.
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