The curvatures of asymptotic lines on a domain of three-dimensional Lobachevsky space that is immersed intoE 5

1994 ◽  
Vol 72 (4) ◽  
pp. 3155-3159
Author(s):  
Yu. A. Aminov
Keyword(s):  
Three Dimensional ◽  
Lobachevsky Space ◽  
Asymptotic Lines

scholarly journals On the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4

2019 ◽  
Vol 486 (1) ◽  
pp. 7-11
Author(s):  
N. V. Bogachev
Keyword(s):  
Three Dimensional ◽  
Reflection Group ◽  
Lobachevsky Space ◽  
Fundamental Polyhedron

In this paper we prove that the fundamental polyhedron of a ℤ2-arithmetic reflection group in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing faces is small enough. Using this fact we obtain a classification of stably reflective hyperbolic ℤ2-lattices of rank 4.

Coherent states on horospheric three-dimensional Lobachevsky space

2016 ◽  
Vol 57 (8) ◽  
pp. 082111 ◽  
Author(s):  
Yu. Kurochkin ◽  
I. Rybak ◽  
Dz. Shoukavy
Keyword(s):  
Coherent States ◽  
Three Dimensional ◽  
Lobachevsky Space

scholarly journals Description of a free quantum-mechanical particle in the Lobachevsky space based on the integral equation

2019 ◽  
Vol 55 (3) ◽  
pp. 319-324
Author(s):  
Yu. A. Kurochkin
Keyword(s):  
Integral Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Separation Of Variables ◽  
Free Particle ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Quantum Mechanical ◽  
Lobachevsky Space

The quantum mechanical problem of the motion of a free particle in the three-dimensional Lobachevsky space is interpreted as space scattering. The quantum case is considered on the basis of the integral equation derived from the Schrödinger equation. The work continues the problem considered in [1] studied within the framework of classical mechanics and on the basis of solving the Schrödinger equation in quasi-Cartesian coordinates. The proposed article also uses a quasi-Cartesian coordinate system; however after the separation of variables, the integral equation is derived for the motion along the axis of symmetry horosphere axis coinciding with the z axis. The relationship between the scattering amplitude and the analytical functions is established. The iteration method and finite differences for solution of the integral equation are proposed.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Sign in / Sign up

Export Citation Format

Share Document