Relating algebraic properties of the curvature tensor to geometry.
Spectral invariants of affine hypersurfaces.
Applications of spectral geometry to affine and projective geometry.
Pseudo-Riemannian Osserman manifolds.
The Residue of the Local Eta Function at the Origin.
Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian
On spherical space forms with meta-cyclic fundamental group which are isospectral but not equivariant cobordant
The eta Invariant and ...O of Lens Spaces.
Spectral Geometry and the Kaehler Condition for Complex Manifolds.
Correction to: Spectral Geometry and the Kaehler Condition for Complex Manifolds.
Local invariants of a pseudo-Riemannian manifold.
The eta invariant and the equivariant unitary bordism of spherical space form groups
The Jordan normal form of higher order Osserman algebraic curvature tensors
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type in a vector space of signature . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
4-Dimensional (Para)-Kähler-Weyl Structures
The Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics
Stanilov-Tsankov-Videv theory.
The eta invariant and metrics of positive scalar curvature.
Complex IP pseudo-Riemannian algebraic curvature tensors
The local index density of the perturbed de Rham complex
A perturbation of the de Rham complex was introduced by Witten for an exact 1-form and later extended by Novikov for a closed 1-form on a Riemannian manifold . We use invariance theory to show that the perturbed index density is independent of ; this result was established previously by J. A. Álvarez López, Y. A. Kordyukov and E. Leichtnam (2020) using other methods. We also show the higher order heat trace asymptotics of the perturbed de Rham complex exhibit nontrivial dependence on . We establish...
Algebraic theory of affine curvature tensors
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.
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