10 citations · 51 across the 21 of their papers we have counts for
22 papers
Harmonic radial vector fields on harmonic spaces
P. B. Gilkey, J. H. Park
We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian on functions and the Laplacian on 1-forms. We exami…
Spaces of locally homogeneous affine surfaces
Miguel Brozos-Vázquez, Eduardo García-Río, Peter Gilkey
We examine the topology of various spaces of locally homogeneous affine manifolds which arise from the classification result of Opozda [B. Opozda, A classification of locally homog…
Applications of PDEs to the study of affine surface geometry
P. Gilkey, X. Valle-Regueiro
If is an affine surface, let be the space of solutions to the quasi-Einstein equation for the…
Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons
M. Brozos-Vázquez, E. García-Río, P. Gilkey
The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connecti…
Anti-invariant Riemannian Submersions
P. Gilkey, M. Itoh, J. H. Park
We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermi…
Real analytic complete non-compact surfaces in Euclidean space with finite total curvature arising as solutions to ODEs
P. Gilkey, C. Y. Kim, J. H. Park
We use the solution space of a pair of ODEs of at least second order to construct a smooth surface in Euclidean space. We describe when this surface is a proper embedding which is…