3 citations · 6 across the 4 of their papers we have counts for
6 papers
The Initial Value Problem for Wave Equation and a Poisson-like Integral in Hyperbolic Plane
F. Catoni, P. Zampetti
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time tri…
Space-time trigonometry and formalization of the "Twin Paradox" for uniform and accelerated motions
Dino Boccaletti, Francesco Catoni, Vincenzo Catoni
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between…
Two-dimensional space-time symmetry in hyperbolic functions
Francesco Catoni, Paolo Zampetti
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex…
Lorentz surfaces with constant curvature and their physical interpretation
Francesco Catoni, Roberto Cannata, Vincenzo Catoni +1
In recent years it has been recognized that the hyperbolic numbers (an extension of complex numbers, defined as z=x+h*y with h*h=1 and x,y real numbers) can be associated to space-…
Hyperbolic trigonometry in two-dimensional space-time geometry
Francesco Catoni, Roberto Cannata, Vincenzo Catoni +1
By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: z=x+h*y with h*h=1 and x,y real numbers. As complex numbers are linked to the Euc…
Integrating the geodesic equations in the Schwarzschild and Kerr space-times using Beltrami's "geometrical" method
Dino Boccaletti, Francesco Catoni, Roberto Cannata +1
We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired…