Related papers: Metallic Structures on Differentiable Manifolds
We construct a multiset space $\mathbb{N}[X]$ over a metric space $X$ that simultaneously enjoys desirable topological properties and admits a natural matching metric $d_{\mathbb{N}[X]}$, making it a metrizable abelian topological monoid…
Topological invariants govern many important physical properties in condensed matter systems. In this work, we obtain the complete set of topological invariants for a family of one-dimensional quasicrystals. The first and best-studied…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and…
We prove that any left-invariant symplectic almost complex structure on a Thurston manifold which is compatible with its canonical left-invariant Riemannian metric has holomorphic type 1.
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own…
This paper studies how many orthogonal bi-invariant complex structures exist on a metric Lie algebra over the real numbers. Recently, it was shown that irreducible Lie algebras which are additionally $2$-step nilpotent admit at most one…
In this paper, we study some properties of warped product pointwise bi-slant submanifolds in locally metallic Riemannian manifolds and we construct some examples in Euclidean spaces.
We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a…
Generalised almost complex structures $\mathcal J$ on transitive Courant algebroids $E$ are studied in terms of their components with respect to a splitting $E\cong TM \oplus T^*M \oplus \mathcal G$, where $M$ denotes the base of $E$ and…
We study 8-dimensional Riemannian manifolds that admit a PSU(3)-structure. We classify these structures by their intrinsic torsion and characterize the corresponding classes via differential equations. Moreover, we consider a connection…
We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved background. The metric…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
We study a recursively defined two-parameter family of graphs which generalize Fibonacci cubes and Pell graphs and determine their basic structural and enumerative properties. In particular, we show that all of them are induced subgraphs of…
Novel ordered intermetallic compounds have stimulated much interest. Ru-Al alloys are a prominent class of high-temperature structural materials, but the experimentally reported crystal structure of the intermetallic Ru2Al5 phase remains…
The chemistry (composition and bonding information) of metallic glasses (MGs) is at least as important as structural topology for understanding their properties and production/processing peculiarities. This article reports a machine…
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.