相关论文: Central potentials on spaces of constant curvature…

The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…

In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature K\"ahler (cscK) metrics. We show this system can be realized variationally as the Euler-Lagrange equation…

We consider a projection from the center of the unit sphere to a tangent space of it, the central projection, and study two area minimizing problems of the image of a closed subset in the sphere. One of the problems is the uniqueness of the…

We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric equivalence between repelling particles and attracting…

In this paper we are concerned with the local well-posedness of the unsteady potential flows near a space corner of right angle, which could be formulated as an initial-boundary value problem of a hyperbolic equation of second order in a…

We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…

Let M be a closed minimal hypersurface in 5-dimensional Euclidean sphere with constant nonnegative scalar curvature. We prove that, if the sum of the cubes of all principal curvatures and the number of distinct principal curvatures are…

Starting from the hypothesis of scaling solutions, the general exact form of the scalar field potential is found. In the case of two fluids, it turns out to be a negative power of hyperbolic sine. In the case of three fluids the analytic…

An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of…

We revisit in this note the H\'enon's isochrone problem. By using the standard Abel inversion technique for one-dimensional motion, we recover in a simple way the H\'enon's parabolae and get all isochrone central potentials under mild…

In this paper, we present a new explicit formula for the curvatures of a regular curve with an arbitrary parameter in the Euclidean space $\mathbb{R}^n$, $n\geq 2$, expressed only in terms of its derivatives. We introduce also the notion of…

The true and eccentric anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits, by considering perturbations of the radial part of the kinetic energy in a form of a series of negative powers of the orbital…

We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time…

We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. However, there exist both special and ordinary central…

In an Euclidean $d$-space, the container problem asks to pack $n$ equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\geq 2$ we show that solutions to the container problem can…

We construct a constant curvature analogue on the two-dimensional sphere ${\mathbf S}^2$ and the hyperbolic space ${\mathbf H}^2$ of the integrable H\'enon-Heiles Hamiltonian $\mathcal{H}$ given by $$…

The additional hidden symmetry of the Coulomb-Kepler problem is reviewed in classical as well as in quantum mechanics. The main purpose is to elucidate the role of this kind of symmetries in the reduction of physical problems, to show…

The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

After a review of the general properties of holomorphic spheres in complex surfaces we describe the local geometry in the vicinity of a CP^1 embedded with a negative normal bundle. As a by-product, we build (asymptotically locally…