arXiv research

The paper studies magnetic curves in $C$-manifolds and their properties.

Study on Killing magnetic curves in Heisenberg group geometry.

A magnetic field is defined by the property that its divergence is zero in a three dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to studies the magnetic flow asociated wit…

Study magnetic curves in Sasakian manifolds, classifying and parametrizing them.

We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space.

Study finds formulas for special curves in complex spaces.

In this paper, we completely classify the magnetic curves (also N-magnetic curves with constant curvature) in a Galilean 3-space associated to a Killing vector field.

We investigate contact magnetic curves in the real special linear group of degree 2. They are geodesics of the Hopf tubes over the projection curve. We prove that periodic contact magnetic curves in SL(2,R) can be quantized in the set of rational numbers. Finally, we study contact homogeneous magnetic trajectories in S…

It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criteri…

Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first establish subconvergence of this flow to a magnetic geodesic under certain boundedness a…

We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.

Homogeneous magnetic trajectories in a special linear group proven.

Study of magnetic geodesics on Heisenberg nilmanifolds.

Study shows finiteness of magnetic hypersurfaces on closed manifolds.

In a three-dimensional Riemannian manifold M that admits a unit Killing vector field $ξ$, we regard $ξ$ as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with $ξ$. Then we characterize Sasakian structure on M from magnetic Hopf surfaces. That is, we show that i…

We give existence results for simple closed curves with prescribed geodesic curvature on $S^{2}$, which correspond to periodic orbits of a charge in a magnetic field.

Study magnetic geodesic flows on spheres, describing their bifurcations.

We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic curvature (also known as magnetic geodesics) on an oriented closed surface. Our results hold when the prescribed curvature is either close t…

For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy le…

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece $γ$ of the boundary must be algebraic and eith…

We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an integral exists then the boundary curve of the domain determines an algebraic curve in…

Study of contact whirl curves in Sasakian Lorentzian 3-manifolds.

We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product…

In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension $\geq 3$ with boundary. We show that one can uniquely determine the conformal factor and the magnetic field near a strictly convex (with respect to the magne…

The study finds lower bounds for the first eigenvalue of the Laplacian in planar domains with magnetic fields.

We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result is a manifestation of the so-called Hopf rigidity phenomenon which was recen…

We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose ex…

The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical bundle of moving frames and the …

The paper develops predictors for functional data on manifolds.

Study electric-magnetic duality in M-theory compactifications.

Study of $p$-biharmonic curves and their properties.

Defines spectral varieties for non-simply connected manifolds and constructs conformal invariants.

It is well-known that the LIE(Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of iso…

Purpose: To construct a neural network model that can learn the different diagnosing strategies of radiologists to better classify aneurysm status in magnetic resonance angiography images. Materials and methods: This retrospective study included 3423 time-of-flight brain magnetic resonance angiography image series (sub…

We relate Gaussian curvature to the gyroscopic force, thus giving a mechanical interpretation of the former and a geometrical interpretation of the latter. We do so by considering the motion of a spinning disk constrained to be tangent to a curved surface. It is shown that the spin gives rise to a force on the disk whi…

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

Extends E. Hopf's theorem to magnetic systems without conjugate points.

Compatibility equations adapted to magnetic geometry.

Wide-band Electromagnetic Induction Sensors (WEMI) have been used for a number of years in subsurface detection of explosive hazards. While WEMI sensors have proven effective at localizing objects exhibiting large magnetic responses, detecting objects lacking or containing very low amounts of conductive materials can b…

We present a novel algorithm that predicts the probability that the time derivative of the horizontal component of the ground magnetic field $dB/dt$ exceeds a specified threshold at a given location. This quantity provides important information that is physically relevant to Geomagnetically Induced Currents (GIC), whic…

This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.

Magnetic Brunn-Minkowski inequalities on Riemannian manifolds

This paper defines directional derivatives and solves Maxwell's equations in curved 3D space.

New tensors help solve magnetic flow integrability.

Study magnetic geodesics on Heisenberg groups and manifolds.

Paper introduces magnetic Hodge Laplacian for differential forms.

Study magnetic Steklov eigenvalues on manifolds with boundary.

Study magnetic potentials on Anosov manifolds using spectral data.