Related papers: Rotation, Embedding and Topology for the Szekeres …
"Diagonal" spatially inhomogeneous (SI) models are introduced under the assumption of the existence of (proper) intrinsic symmetries and can be seen, in some sense, complementary to the Szekeres models. The structure of this class of…
Symmetry plays a vital role in understanding structural patterns, aiding object recognition and scene interpretation. This paper focuses on rotation symmetry, where objects remain unchanged when rotated around a central axis, requiring…
A trajectory $u_n := F^n(u_0), n = 0,1,2, \dots $ is quasiperiodic if the trajectory lies on and is dense in some $d$-dimensional torus, and there is a choice of coordinates on the torus $\mathbb{T}$ for which $F$ has the form $F(\theta) =…
Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two `self-equilibrated' states, one natural and the other inside out (or `everted'). Though this is…
In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type…
We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott's model of rotation. It…
In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our result shows that if a geometric hexagonal triangulation of the…
We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those…
In the present article, we investigate the topology of real toric varieties, especially those whose torus is not split over the field of real numbers. We describe some canonical fibrations associated to their real loci. Then, we establish…
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…
A family of embedded rotationally symmetric tori in the Euclidean 3-space consisting of two opposite signed constant mean curvature surfaces that converge as varifolds to a double round sphere is constructed. Using complete elliptic…
In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning, (b) the further transfer of these results to spherical space via associated…
We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge…
A novel spin texture formed by Cooper pair spins is found theoretically with a phase string attached by half-quantized vortices at both ends in a unit cell and characterized by its topologically rich vortex structure in a spin-triplet…
Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems - in Kodama-Schwarzschild coordinates and in Gaussian normal coordinates. We consider transformations between the coordinate systems as in…
We study coherent optics in topological insulator surface states with broken time-reversal symmetry and develop a theory for the dynamical Hall effect driven by intense electromagnetic field. The influence of optical Stark effect enters as…
We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…
We study the dynamics of a circular passive inclusion, termed a torquer, in a bath of chiral active Brownian particles. Despite being geometrically symmetric and non-motile, the torquer exhibits persistent rotation due to spatially…
We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric…
The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state that two of these can only agree in the K\"ahler case. Our…