Related papers: Equivariant isospectrality and Sunada's Method

A singular foliation on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal,…

This paper explores the existence and properties of \emph{basic} eigenvalues and eigenfunctions associated with the Riemannian Laplacian on closed, connected Riemannian manifolds featuring an effective isometric action by a compact Lie…

We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are…

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k\le n-3. The smooth Yamabe invariants \sigma(M) and \sigma(N) satisfy \sigma(N)\ge min (\sigma(M),\Lambda) for \Lambda>0. We…

In this work we construct new multidimensional families of complete minimal submanifolds, of the classical non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(2n)/U(n) and SU*(2n)/Sp(n), of codimension two.

We continue our exploration of the extent to which the spectrum encodes the local geometry of a locally homogeneous three-manifold and find that if $(M,g)$ and $(N,h)$ are a pair of locally homogeneous, locally non-isometric isospectral…

Lying at the intersection of Ado's theorem and the Nash embedding theorem, we consider the problem of finding faithful representations of Lie groups which are simultaneously isometric embeddings. Such special maps are found for a certain…

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in $\rn$. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier…

We extend the methods of Davis-Januszkiewicz-Lafont to provide a new obstruction to smooth Riemannian metric with non-positive sectional curvature. We construct examples of locally CAT(0) 4-manifolds $M$, whose universal covers satisfy…

Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in…

We determine the spectrum of the sub-Laplacian on pseudo H-type nilmanifolds and present pairs of isospectral but non-diffeomorphic nilmanifolds with respect to the sub-Laplacian. We observe that these pairs are also isospectral with…

We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the…

For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence not locally homogeneous. All the local scalar Weyl invariants…

We give obstructions for a noncompact manifold to admit a complete Riemannian metric with (nonuniformly) positive scalar curvature. We treat both the finite volume and infinite volume cases.

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.

We study in this paper previously defined by V.N. Berestovskii and C.P. Plaut $\delta$-homogeneous spaces in the case of Riemannian manifolds. Every such manifold has non-negative sectional curvature. The universal covering of any…

The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian…

In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of…

We consider a random family of Schr\"odinger operators on a cover $X$ of a compact Riemannian manifold $M = X/\Gamma$. We present several results on their spectral theory, in particular almost sure constancy of the spectral components and…