Isospectral Conformal Metrics on 3 - Manifolds
نویسنده
چکیده
Theorem. Let gj = u;go be a sequence of conformal metrics satisfying the following conditions. (i) Vol(M, g) = eto for some positive constant eto. (ii) f R2(g) + Ip(gj)1 2 dJj ::; et2 for some positive constant et2 where R(g) is the scalar curvature of gj and p is the Ricci tensor of gj and dJj = u~ dVO. (iii) Al (g), the lowest eigenvalue of the Laplacian of the metric gj' has a positive lower bound: Al (g) ~ A > 0; i.e., for each ¢ defined on M, we have
منابع مشابه
Isospectral Metrics and Potentials on Classical Compact Simple Lie Groups
Given a compact Riemannian manifold (M,g), the eigenvalues of the Laplace operator ∆ form a discrete sequence known as the spectrum of (M,g). (In the case the M has boundary, we stipulate either Dirichlet or Neumann boundary conditions.) We say that two Riemannian manifolds are isospectral if they have the same spectrum. For a fixed manifold M , an isospectral deformation of a metric g0 on M is...
متن کاملEquivariant Isospectrality and Isospectral Deformations of Metrics on Spherical Orbifolds
Most known examples of isospectral manifolds can be constructed through variations of Sunada’s method or Gordon’s torus method. In this paper we explore these two techniques in the framework of equivariant isospectrality. We begin by establishing an equivariant version of Sunada’s technique and then we observe that many examples arising from the torus method are equivariantly isospectral. Using...
متن کاملCornucopia of Isospectral Pairs of Metrics on Balls and Spheres with Different Local Geometries
This article is the second part of a comprehensive study started in [Sz4], where the first isospectral pairs of metrics are constructed on balls, spheres, and other manifolds by a new isospectral construction technique, called ”Anticommutator Technique”. In this paper we reformulate this Technique in its most general form and we determine all the isospectral deformations provided by this method...
متن کاملConformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملThe conformal analog of Calabi-Yau manifolds
This survey intends to introduce the reader to holonomy theory of Cartan connections. Special attention is given to the normal conformal Cartan connection, uniquely defined for a class of conformally equivalent metrics, and to its holonomy group the ’conformal holonomy group’. We explain the relation between conformal holonomy group and existence of Einstein metrics in the conformal class as we...
متن کامل