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A new proof of a theorem that describes (, ) -eigenfunctions on sphere is obtained. This proof is based on a statement that a function f is a (, ) -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 ₍, ₌ surfaces are described in terms of (, ) -eigenfunctions.
Aleksei Kislitsyn (Fri,) studied this question.