相关论文: Killing magnetic curves in non-flat Lorentzian-Hei…

In this paper, We present the geometry three dimensional Heisenberg group (H_3,g) and its geodesics curves. After, we study the Killing magnetic curves and some geodesic Killing magnetic curves with its explicit formulas for such curves.

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

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.

In this paper, we study classification of magnetic curves corresponding to Killing vector fields of H^3 (hyperbolic 3-space). First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six…

Conformal Killing equations and their integrability conditions for nonexpanding hyperheavenly spaces with Lambda are studied. Reduction of ten Killing equations to one master equation is presented. Classification of homothetic and isometric…

Assuming the stability of soliton surfaces of vanishing Ricci sectional curvature of soliton metric in the nonholonomic frame, we find a solution for the metric in the approximation of weak constant torsion curves with constant Frenet…

We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any timelike curvature bound, either from above or below, and…

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…

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…

We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the…

We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. Spaces of constant…

We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil…

New exact solutions of the steady and incompressible 2D MHD equations in polar coordinates are presented. The solutions describe the process of reconnective magnetic annihilation in a curved current layer. They are particularly interesting…

Using an explicit version of the Mumford isomorphism on the moduli space of hyperelliptic curves we derive a closed formula for the Arakelov-Green function of a hyperelliptic Riemann surface evaluated at its Weierstrass points.

We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the…

We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on…

We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static…

A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvin's magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The…

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the…

We formulate a uniqueness conjecture for curve shortening flow of proper curves on certain symmetric surfaces and give an example of a non-flat metric on the plane with respect to which curve shortening flow is not unique. That is, with…