相关论文: Rotation, Embedding and Topology for the Szekeres …

We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…

Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…

We study the shape dependence of entanglement entropy (EE) by deforming symmetric entangling surfaces. We show that entangling surfaces with a rotational or translational symmetry extremize (locally) the EE with respect to shape…

We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also…

Following a survey of the abstract boundary definition of Scott and Szekeres, a rigidity result is proved for the smooth case, showing that the topological structure of the regular part of this boundary in invariantly defined.

We study the behavior of the Gieseker space of semistable torsion-free sheaves of rank r and fixed c_1, c_2 on a non-singular projective surface as the polarization varies. It is shown that the ample cone admits a locally finite chamber…

The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…

Many obsects in the solar system are suspected to have experience reorientation of their spin axes. As their rotation rates are slow and their shapes are nearly spherical, the formation of mass anomalies, by either endogenic of exogenic…

When the Rayleigh number is low, Rayleigh-B\'enard convection in a nonrotating spherical shell with central gravity has symmetric solutions in terms of three-dimensional discrete rotation. All the known patterns with the regular polyhedral…

In the context of $\theta$ electrodynamics we find transverse electromagnetic wave solutions forbidden in Maxwell electrodynamics. Our results attest to new evidence of the topological magnetoelectric effect in topological insulators,…

This paper is devoted to topological phenomena in normal metals with rather complicated Fermi surface. The results of the article are based on the deep topological theorems concerning the geometry of non-compact plane sections of level…

Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…

Total rotation is a quantity that has been used for years in RSA. However, its definition has no mathematical sense, since the Euler angles do not form a vector space, since angles cannot define a multiplication group. With this work I…

We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data…

Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable…

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are…

In this work we study regular black holes from a global perspective looking for evading some of the well-known singularity theorems by using their "reverses". Then, model geometries for the slices of typical spherically symmetric, (locally)…

Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…

Slowly rotating collapsing spherical shells have flat spaces inside and the inertial frames there rotate at omega_s(t) relative to infinity. As first shown by Lindblom & Brill the inertial axes within the shell rotate rigidly without time…

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally…