Related papers: Foliations induced by metallic structures

It is shown that metamagnetic transition in metals can occur via the formation of electronic nematic order. We consider a simple model where the spin-dependent Fermi surface instability gives rise to the formation of an electronic nematic…

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…

This paper presents a simplified geometric proof of the Molino-Alexandrino-Radeschi (MAR) Theorem, which states that the closure of a singular Riemannian foliation on a complete Riemannian manifold is itself a smooth singular Riemannian…

Crack-templated networks, metallic frameworks fabricated from crack patterns in sacrificial thin films, can exhibit high optical transmittance, high electric conductivity, and a host of other properties attractive for applications. Despite…

In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold,…

We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order.…

We use the cosmological semi-analytic model (SAM) for galaxy formation presented in Paper I to study the metallicities and abundance ratios of the intracluster medium (ICM) within the hierarchical structure formation paradigm. By requiring…

A transitive compact foliated space is shown to be a Riemannian foliation if and only if it is locally connected, finite dimensional, strongly equicontinuous and quasi-analytic, and the closure of its holonomy pseudogroup is quasi-analytic.

Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify such…

On an orientable manifold M, we consider a regular even dimensional foliation F which is globally defined by a set of k-independent 1-forms. We give necessary and sufficient conditions for the existence of a regular Poisson structure on M…

The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…

We prove that a foliation $(M, F)$ of codimension $q$ on a $n$-dimen\-sio\-nal pseudo-Riemannian manifold is pseudo-Riemannian if and only if any geodesic that is orthogonal at one point to a leaf is orthogonal to every leaf it intersects.…

A Riemannian symmetric space is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. On such spaces, we introduce the notion of a distributional lattice, generalizing the notion…

In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved…

The lattice dynamics of the metallic tin {\beta} and {\gamma} polymorphs has been studied by a combination of diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. The non-symmorphic space group of the…

Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…

We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence…

The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a…

In this work we investigate the transport properties of non-relativistic quantum particles on incommensurate multilayered structures with the thicknesses $w_n$ of the layers following an extended Harper model given by $w_n = w_0 |\cos(\pi a…

We prove that if a geodesic metric measure space satisfies a comparison condition for isoperimetric profile and if the observable variance is maximal, then the space is foliated by minimal geodesics, where the observable variance is defined…