Related papers: Flat Manifolds Isospectral on p-Forms

In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…

The first isospectral pairs of metrics are constructed on balls and spheres. This long standing problem, concerning the existence of such pairs, has been solved by a new method called "Anticommutator Technique." Among the wide range of such…

We pose the isospectral problem for the $p$-widths: Is a riemannian manifold $(M^n, g)$ uniquely determined by its $p$-widths, $\{\omega_p(M,g)\}_{p=1}^{\infty}$? We construct many counterexamples on $S^2$ using Zoll metrics and the fact…

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the…

Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…

We study the moduli spaces of flat SL(r)- and PGL(r)-connections, or equivalently, Higgs bundles, on an algebraic curve. These spaces are noncompact Calabi-Yau orbifolds; we show that they can be regarded as mirror partners in two different…

We compute the topological simple structure set of closed manifolds which occur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an n-dimensjional torus T^n for an odd prime p and l greater or equal to 3, provided that…

We consider a family of compact, oriented and connected Riemannian manifolds shrinking to a metric graph and describe the asymptotic behaviour of the eigenvalues of the Hodge Laplacian. We apply our results to produce manifolds with…

We construct isospectral pairs of Riemannian metrics on S^5 and on B^6, thus lowering by three the dimension of spheres and balls on which such metrics have been constructed previously (S^{n\ge 8} and B^{n\ge 9}). We also construct…

In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth…

We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace operator acting on functions. These are the…

A bi-Hamiltonian structure is a pair of Poisson structures $\mathcal P$, $\mathcal Q$ which are compatible, meaning that any linear combination $\alpha \mathcal P + \beta \mathcal Q$ is again a Poisson structure. A bi-Hamiltonian structure…

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a…

Let $G \to P \to M$ be a flat principal bundle over a closed and oriented manifold $M$ of dimension $m=2d$. We construct a map of Lie algebras $\Psi: \H_{2\ast} (L M) \to {\o}(\Mc)$, where $\H_{2\ast} (LM)$ is the even dimensional part of…

Let $M$ be a real $l$-dimensional minimal submanifold with flat normal connection in a kaehler product manifold $\overline{M}^m\times \overline{M}^n$ where $\overline{M}^m$ and $\overline{M}^n$ are complex $m$-dimensional and complex…

By a recent observation, the Laplacians on the Riemannian manifolds the author used for isospectrality constructions are nothing but the Zeeman-Hamilton operators of free charged particles. These manifolds can be considered as prototypes of…

We construct examples of flat fiber bundles over the Hopf surface such that the total spaces have no pseudoconvex neighborhood basis, admit a complete K\"ahler metric, or are hyperconvex but have no nonconstant holomorphic functions. For…

The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we…

We obtain geometric estimates for the first eigenvalue and the fundamental tone of the p-laplacian on manifolds in terms of admissible vector fields. Also, we defined a new spectral invariant and we show its relation with the geometry of…

Given a manifold (or, more generally, a developable orbifold) $M_0$ and two closed Riemannian manifolds $M_1$ and $M_2$ with a finite covering map to $M_0$, we give a spectral characterisation of when they are equivalent Riemannian covers…