Class of equivalent equations

Abstract

It is shown that, for certain second-order linear homogeneous partial differential equations, there exists a set of equivalence transformations to the form Δ₂u+c′(x)u = 0 in the metric of spaces conformal to the space V_n related to the equation. An element of this space is a transformation of the equation to the canonical form

$$\Delta _2 u + \frac{{n - 2}}{{4(n - 1)}}Ru = \pm u$$

in the metric of a space V′_n, where R is the scalar curvature of V′_n. Examples are examined of equations reducible to canonical form in spaces of constant curvature and in Kagan's subprojective space. The bibliography contains five references.