Minimal submanifolds in spheres and complex-valued eigenfunctions

A new proof of a theorem that describes (λ, μ)-eigenfunctions on sphere is obtained. This proof is based on a statement that a function f is a (λ, μ)-eigenfunction if and only if f and f² are eigenfunctions for Laplace-Beltrami operator. Also, minimal submanifolds in spheres of codimension 1 are constructed. In the case of S³ two immersions of Clifford torus and all Lawson τn, m surfaces are described in terms of (λ, μ)-eigenfunctions.