17 citations · 125 across the 54 of their papers we have counts for
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math.DG2007★ 1 cited
The classification of simple Jacobi--Ricci commuting algebraic curvature tensors
P. Gilkey, S. Nikcevic
We classify algebraic curvature tensors such that the Ricci operator is simple (i.e. the Ricci operator is complex diagonalizable and either the complex spectrum consists of a sing…
math.DG2007★ 7 cited
Examples of signature (2,2) manifolds with commuting curvature operators
M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey +1
We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the…
math.DG2007
Projectively Osserman manifolds
M. Brozos-Vazquez, P. Gilkey, S. Nikcevic +1
One says that a smooth manifold M is a pseudo-Riemannian manifold of signature (p,q) if the tangent bundle TM is equipped with a smooth non-degenerate symmetric inner product g of…