17 citations · 75 across the 35 of their papers we have counts for
6 papers · 1 filter
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…
Heat trace asymptotics with singular weight functions
M. van den Berg, P. Gilkey, K. Kirsten +1
We study the weighted heat trace asymptotics of an operator of Laplace type with Dirichlet boundary conditions where the weight function exhibits radial blowup. We give formulas fo…
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…
Heat content
M. van den Berg, P. Gilkey, R. Seeley
We study the heat content asymptotics with either Dirichlet or Robin boundary conditions where the initial temperature exhibits radial blowup near the boundary. We show that there…
Heat Content, Heat Trace, and Isospectrality
Peter B. Gilkey
We study the heat content function, the heat trace function, and questions of isospectrality for the Laplacian with Dirichlet boundary conditions on a compact manifold with smooth…
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…