17 citations · 72 across the 27 of their papers we have counts for
7 papers · 1 filter
The Spectral Geometry of the Riemann Curvature Operator in the Higher Signature Setting
C. Dunn, P. Gilkey, R. Ivanova +1
We study the spectral geometry of the Riemann curvature tensor for Pseudo-Riemannian manifolds and provide some examples illustrating the phenomena which can arise in the higher si…
Eigenforms of the Laplacian for Riemannian V-submersions
Peter B. Gilkey, Hong-Jong Kim, JeongHyeong Park
Let p: Z -> Y be a Riemannian V-submersion of compact V-manifolds. We study when the pull-back of an eigenform of the Laplacian on Y is an eigenform of the Laplacian on Z, and when…
The spectral geometry of the Weyl conformal tensor
N. Blazic, P. Gilkey, S. Nikcevic +1
We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads…
Manifolds which are Ivanov-Petrova or k-Stanilov
P. Gilkey, S. Nikcevic, V. Videv
We present some examples of curvature homogeneous pseudo-Riemannian manifolds which are k-spacelike Jordan Stanilov; their higher order curvature operator has constant Jordan norma…
Curvature homogeneous pseudo-Riemannian manifolds which are not locally homogeneous
Corey Dunn, Peter B Gilkey
We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric…
Heat content, torsional rigidity and generalized Hardy inequalities for complete Riemannian manifolds
Michiel van den Berg, Peter B. Gilkey
We obtain upper bounds on the heat content and on the torsional rigidity of a complete Riemannian manifold M, assuming a generalized Hardy inequality for the Dirichlet Laplacian on…