On the generic spectrum of a riemannian cover

Steven Zelditch

Displaying similar documents to “On the generic spectrum of a riemannian cover”

On the spectrum of Riemannian submersions with totally geodesic fibers

Gérard Besson, Manlio Bordoni (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.

Isospectral deformations of closed riemannian manifolds with different scalar curvature

Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson (1998)

Annales de l'institut Fourier

Similarity:

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on $S^{n} \times T^{m}$ , where $T^{m}$ is a torus of dimension $m \geq 2$ and $S^{n}$ is a sphere of dimension $n \geq 4$ . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

Geometry of manifolds which admit conservation laws

David E. Blair, Alexander P. Stone (1971)

Annales de l'institut Fourier

Similarity:

Let $M$ be an $(n + 1)$ -dimensional Riemannian manifold admitting a covariant constant endomorphism $h$ of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that $M$ is locally flat, a manifold $N$ immersed in $M$ is studied. The manifold $N$ has an induced structure with $n$ of the same eigenvalues if and only if the normal to $N$ is a fixed direction of $h$ . Finally conditions under which $N$ is invariant under $h$ , $N$ is totally geodesic and the induced structure has vanishing...

Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations

Alexandru Kristály, Vicenţiu Rădulescu (2009)

Studia Mathematica

Similarity:

Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem $- Δ_{g} ω + α (σ) ω = K ̃ (λ, σ) f (ω)$ , σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, $Δ_{g}$ stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These...

The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold

Hajime Urakawa (1986)

Compositio Mathematica

Similarity:

High-order angles in almost-Riemannian geometry

Ugo Boscain, Mario Sigalotti (2006-2007)

Séminaire de théorie spectrale et géométrie

Similarity:

Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$ . If $X$ and $Y$ are everywhere linearly independent, then they define a Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$ , then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally...