19 citations · 42 across the 10 of their papers we have counts for
10 papers
Harmonic Variables for Laplace Operators on Homogeneous Spaces
I. V. Shirokov
A definition of harmonic variables for Laplace operators on Riemannian and pseudo-Riemannian spaces is introduced. Harmonic variables allow, in particular, the construction of part…
Classification of scalar second-order differential equations with low-dimensional symmetry groups: The case of free action
Alexey A. Magazev, Igor V. Shirokov
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations w…
Algebraic method for construction of infinitesimal invariants of Lie groups representations
Oleg L. Kurnyavko, Igor V. Shirokov
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is…
A method of integration for classical and quantum equations based on the connection between canonical transformations and irreducible representations of Lie groups
Alexey A. Magazev, Igor V. Shirokov
We propose a method for integrating the right-invariant geodesic flows on Lie groups based on the use of a special canonical transformation in the cotangent bundle of the group. We…
Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
Alexey A. Magazev, Vitaly V. Mikheyev, Igor V. Shirokov
Methods of construction of the composition function, left- and right-invariant vector fields and differential 1-forms of a Lie group from the structure constants of the associated…
Integration of geodesic flows on homogeneous spaces: the case of a wild lie group
A. A. Magazev, I. V. Shirokov
We obtain necessary and sufficient conditions for the integrability in quadratures of geodesic flows on homogeneous spaces with invariant and central metrics. The proposed inte…