相关论文: Quadrangles embedded in metasymplectic spaces
Self-similar quasicrystals (like the famous Penrose and Ammann-Beenker tilings) are exceptional geometric structures in which long-range order, quasiperiodicity, non-crystallographic orientational symmetry, and discrete scale invariance are…
Let $M^n$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function…
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: given a submanifold of configurations of points on an embedding of a compact manifold $M$ in…
We show that, for Finsler spaces with cubic metric, Landsberg spaces are Berwaldian. Also, for decomposable metrics, we determine specific conditions for a space with cubic metric to be of Berwald type, thus refining the result in [6].
Li, Ma and Wang have provided in [\emph{Deformations of hypersurfaces preserving the M\"obius metric and a reduction theorem}, Adv. Math. 256 (2014), 156--205] a partial classification of the so-called Moebius deformable hypersurfaces, that…
Hyperbolic buildings are central objects in both hyperbolic geometry and geometric group theory, exhibiting a wide range of intriguing characteristics, especially with respect to group actions. In this paper, we develop the theory of…
Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these…
We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edge-to-edge tilings of the sphere by congruent equilateral…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…
We review the regular tilings of d-sphere, Euclidean d-space, hyperbolic d-space and Coxeter's regular hyperbolic honeycombs (with infinite or star-shaped cells or vertex figures) with respect of possible embedding, isometric up to a scale,…
A simple proof is given of the following result first observed by J. Adachi: embedded circles tangent to the standard Engel structure on Euclidean 4-space are classified, up to isotopy via such embeddings, by their rotation number.
We construct examples of complete quaternionic K\"ahler manifolds with an end of finite volume, which are not locally homogeneous. The manifolds are aspherical with fundamental group which is up to an infinite cyclic extension a semi-direct…
In earlier work (*) we studied an extension of the canonical symplectic structure in the cotangent bundle of an affine space ${\cal Q}={\bf R}^N$, by additional terms implying the Poisson non-commutativity of both configuration and momentum…
We consider the following question: When does a Riemannian manifold admit an embedding with a uniformly thick tubular neighborhood in another Riemannian manifold of large dimension?
Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the…
4-dimensional $F_{4} $ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an…
We show there exists a rigid monoidal category formed out by quantum linear spaces with an additional structure, such that FRT bialgebras and corresponding rectangular generalizations are its internal coEnd and coHom objects, respectively.…
In the article [\emph{Deformations of hypersurfaces preserving the M\"obius metric and a reduction theorem}, Adv. Math. 256 (2014), 156--205], Li, Ma and Wang investigated the interesting class of Moebius deformable hypersurfaces, that is,…
Let $M$ be a strictly convex smooth connected hypersurface in $\mathbb R^n$ and $\widehat{M}$ its convex hull. We say that $M$ is locally polynomially integrable if the $(n-1)-$ dimensional volumes of the sections of $\widehat M$ by…
We give an overview of some recent results in hypersymplectic and para-quaternionic Kahler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of…