17 citations · 143 across the 72 of their papers we have counts for
4 papers · 2 filters
Affine Killing complete and geodesically complete homogeneous affine surfaces
P. B. Gilkey, J. H. Park, X. Valle-Regueiro
An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine K…
Constructing Bach Flat Manifolds of signature using the modified Riemannian extension
E. Calviño-Louzao, E. García-Río, P. Gilkey +2
We use the modified Riemannian extension of an affine surface to construct Bach flat manifolds. As all these examples are VSI (vanishing scalar invariants), we shall construct scal…
Solutions to the affine quasi-Einstein equation for homogeneous surfaces
M. Brozos-Vázquez, E. García-Río, P. Gilkey +1
We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, co…
Affine surfaces which are Kähler, para-Kähler, or nilpotent Kähler
E. Calviño-Louzao, E. García-Río, P. Gilkey +2
Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace free tensors of type on an affine surface. It is sh…