17 citations · 75 across the 35 of their papers we have counts for
10 papers · 2 filters
Jordan Szabo algebraic covariant derivative curvature tensors
Peter B. Gilkey, Raina Ivanova, Iva Stavrov
We show that if is a Jordan Szabo algebraic covariant derivative curvature tensor on a vector space of signature (p,q), where q is odd and p is less than q or if q is co…
The spectral geometry of the Riemann curvature tensor
P. Gilkey, R. Ivanova, T. Zhang
Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan nor…
Szabo Osserman IP Pseudo-Riemannian manifolds
Peter Gilkey, Raina Ivanova, Tan Zhang
We construct a family of pseudo-Riemannian manifolds so that the skew-symmetric curvature operator, the Jacobi operator, and the Szabo operator have constant eigenvalues on their d…
The Geometry of the Skew-Symmetric Curvature Operator in the Complex Setting
Peter Gilkey, Raina Ivanova
We construct almost complex algebraic curvature tensors for pseudo Hermitian inner products whose skew-symmetric curvature operator has constant Jordan normal form on the set of no…
Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2
Peter Gilkey, Tan Zhang
Let R be an algebraic curvature tensor for a non-degenerate inner product of signature(p,q) where q>4. If is a spacelike 2 plane, let be the associated skew-symmetric cu…
Algebraic curvature tensors for indefinite metrics whose skew-symmetric curvature operator has constant Jordan normal form
Peter Gilkey, Tan Zhang
We classify the connected pseudo-Riemannian manifolds of signature with so that at each point of the skew-symmetric curvature operator has constant rank 2 and c…