In this paper, a group model for real extension of the de Sitter plane is pro-posed. This contains special matrices, which subgroup general linear group. It established that there exists left-invariant contact metric structure on group, normal and, therefore, para-Sasakian. The basis vector fields Lie algebra infinitesimal automorphisms are found. has maximum dimension in addition to Levi-Civit...

Abstract. The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the LeviCivita transformation. These connections lead to an approach to solve the Coulomb problems using the results of the harmonic oscillator potential in the above...

The analytic expression of the momentum representation in terms of the associated Legendre function is determined by a direct integration of Fourier transform of the wave function of coordinates using the Levi-Civita transformation and 2 2 R R → the generating function method. A new generating function for the associated Legendre functions are obtained.