17 citations · 115 across the 49 of their papers we have counts for
5 papers · 2 filters
Geometric Realizations of Hermitian curvature models
M. Brozos-Vazquez, P. Gilkey, H. Kang +1
We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature…
Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators
P. Gilkey, S. Nikcevic, D. Westerman
We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at…
Geometric realizations of generalized algebraic curvature operators
P. Gilkey, S. Nikcevic, D. Westerman
We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projecti…
Four-dimensional Osserman metrics of neutral signature
E. Garcia-Rio, P. Gilkey, M. E. Vazquez-Abal +1
In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null…
Geometrical representations of equiaffine curvature operators
Peter B. Gilkey, Stana Nikcevic
We examine geometric representability results for various classes of equiaffine curvature operators. We show every Ricci flat algebraic curvature operator is geometrically realizab…