6 citations · 7 across the 8 of their papers we have counts for
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The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting
C. Dunn, P. Gilkey, R. Ivanova +1
We study the spectral geometry of the Riemann curvature tensor for Pseudo-Riemannian manifolds and provide some examples illustrating the phenomena which can arise in the higher si…
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…
Complex IP curvature tensors
Peter Gilkey, Raina Ivanova
Let M be a pseudo-Riemannian manifold with a pseudo-Hermitian complex structure . We give necessary and sufficient conditions that the curvature operator is complex linea…