Related papers: Massive particle surfaces, partial umbilicity and …
We study the geodesic motion of massless particles in singly rotating black ring spacetimes. We find stable stationary orbits of massless particles in toroidal spiral shape in the case that the thickness parameter of a black ring is less…
Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral surfaces, is characterized by their monodromy groups,…
A mathematical model (referred as $\Psi$ - model for convenience) has been developed, which allows describing certain class of micro- and macrosystems. $\Psi$ - model is based on continuum and quantum mechanics. $\Psi$ - model describes…
We deal with minimal surfaces in spheres that are locally isometric to a pseudoholomorphic curve in a totally geodesic $\mathbb{S}^{5}$ in the nearly K{\"a}hler sphere $\mathbb{S}^6$. Being locally isometric to a pseudoholomorphic curve in…
We show that to every maximal surface with conelike singularities in Lorentz-Minkowski space $\mathbb{L}^3$ that can be locally represented as the graph of a smooth function, there exists a corresponding timelike minimal surface in…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude…
This paper establishes the geometric structure of the lines of principal curvature of a hypersurface immersed in ${\mathbb R}^4$ in a neighborhood of the set $\mathcal{S}$ of its principal curvature singularities, consisting of the points…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta. We also show that some of these metrics can be extended to the 2-sphere.…
Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element…
MOG as a modified gravity theory is designed to be replaced with dark matter. In this theory, in addition to the metric tensor, a massive vector is a gravity field where each particle has a charge proportional to the inertial mass and…
We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature…
The Riemannian product $\mathbb M_1(c_1) \times \mathbb M_2(c_2)$, where $\mathbb M_i(c_i)$ denotes the $2$-dimensional space form of constant sectional curvature $c_i \in \mathbb R$, has two different Spin$^c$ structures carrying each a…
We investigate the bound orbits of massive/massless, neutral particles and photons moving around regular black holes of Fan and Wang. For massive particles, we show the existence of stable/unstable circular orbits and the charge dependence…
It has been long known that in spacetimes with a positive cosmological constant $\Lambda >0$ the area of spatially stable marginally trapped surfaces (MTSs) has a finite upper bound given by $4\pi/\Lambda$. In this paper I show that any…
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing…
We characterize isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous space. These…
We obtain a full resolution result for minimizers in the exterior isoperimetric problem with respect to a compact obstacle in the large volume regime $v\to\infty$. This is achieved by the study of a Plateau-type problem with free boundary…
Conditions for the existence of repeatable light paths (RLPs) in the shearfree normal cosmological models are investigated. It is found that in the conformally nonflat models the only RLPs are radial null geodesics (in the spherical case)…