Related papers: Locally Isotropic Pseudo-Riemannian Manifolds

We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by…

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…

In this work we study riemannian metrics on flag manifolds adapted to the symmetries of these homogeneous nonsymmetric spaces. We first introduce the notion of riemannian $\Gamma $-symmetric space when $\Gamma $ is a general abelian finite…

Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of…

We derive a stochastic representation for determinants of Laplace-type operators on vectors bundles over manifolds. Namely, inverse powers of those determinants are written as the expectation of a product of holonomies defined over Brownian…

In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=\phi…

On the unit tangent bundle of a compact Riemannian surface of constant nonzero curvature, we study semiclassical Schr{\"o}dinger operators associated with the natural sub-Riemannian Laplacian built along the horizontal bundle. In that setup…

For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on…

Radial eigenfunctions of the Laplace-Beltrami operator on compact rank-one symmetric spaces may be expressed in terms of Jacobi polynomials. We use this fact to prove an identity for Jacobi polynomials which is inspired by results of…

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions…

We study eigenvalue problems for intrinsic sub-Laplacians on regular sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues $\lambda_k$ of conformal sub-Riemannian metrics that are asymptotically sharp as $k\to…

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…

We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove…

In the local gluing one glues local neighborhoods around the critical point of the stable and unstable manifolds to gradient flow lines defined on a finite time interval $[-T,T]$ for large $T$. If the Riemannian metric around the critical…

We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the…

The main objective of this paper is to analyze the $p$-local homotopy type of the complex projective Stiefel manifolds, and other analogous quotients of Stiefel manifolds. We take the cue from a result of Yamaguchi about the $p$-regularity…

In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…

We study decay and smoothness properties for eigenfunctions of compact localization operators. Operators with symbols a in the wide modulation space M^{p,\infty} (containing the Lebesgue space L^p), p<\infty, and windows \f_1,\f_2 in the…

We study the eigenvalues and eigenfunctions of a differential operator that governs the asymptotic behavior of the unsupervised learning algorithm known as Locally Linear Embedding when a large data set is sampled from an interval or disc.…

We introduce and investigate symmetric operators $L_0$ associated in the complex Hilbert space $L^2(\mathbb{R})$ with a formal differential expression \[l[u] :=-(pu')'+qu + i((ru)'+ru') \] under minimal conditions on the regularity of the…