14 citations · 31 across the 9 of their papers we have counts for
9 papers
Manifolds with commuting Jacobi operators
M. Brozos-Vazquez, P. Gilkey
We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.
Isometry groups of k-curvature homogeneous pseudo-Riemannian manifolds
P. Gilkey, S. Nikcevic
We study the isometry groups and Killing vector fields of a family of pseudo-Riemannian metrics on Euclidean space which have neutral signature (3+2p,3+2p). All are p+2 curvature h…
Generalized plane wave manifolds
Peter Gilkey, Stana Nikcevic
We show that generalized plane wave manifolds are complete, strongly geodesically convex, Osserman, Szabo, and Ivanov-Petrova. We show their holonomy groups are nilpotent and that…
Conformally Osserman manifolds and self-duality in Riemannian geometry
Novica Blazic, Peter Gilkey
We study the spectral geometry of the conformal Jacobi operator on a 4-dimensional Riemannian manifold (M,g). We show that (M,g) is conformally Osserman if and only if (M,g) is sel…
Affine curvature homogeneous 3-dimensional Lorentz Manifolds
P. Gilkey, S. Nikcevic
We study a family of 3-dimensional Lorentz manifolds. Some members of the family are 0-curvature homogeneous, 1-affine curvature homogeneous, but not 1-curvature homogeneous. Some…
Complete k-curvature homogeneous pseudo-Riemannian manifolds 0-modeled on an indecomposible symmetric space
Peter Gilkey, Stana Nikcevic
For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogene…