9 citations · 17 across the 7 of their papers we have counts for
7 papers
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…
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…
Curvature homogeneous signature (2,2) manifolds
C. Dunn, P. Gilkey, S. Nikcevic
We exhibit a family of generalized plane wave manifolds of signature (2,2). The geodesics in these manifolds extend for infinite time (i.e. they are complete), they are spacelike a…
Complete k-curvature homogeneous pseudo-Riemannian manifolds
P. Gilkey, S. Nikcevic
For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence n…