Finite type minimal 2-spheres in a complex projective space (Q1335274)

The author studies minimal 2-spheres \(M\) immersed in the complex projective space \(\mathbb{C} P^ m\) such that the first eigenfunctions of \(\mathbb{C} P^ m\), when restricted to \(M\), decompose into a finite sum of eigenfunctions of \(M\). First he proves that a certain known family of minimally immersed spheres satisfies the property above, and then he gives a characterization of some surfaces in that family in terms of the existence of this finite decomposition. The author also observes the following curious fact: if, given a compact submanifold \(M\) of \(\mathbb{C} P^ m\), any first eigenfunction of \(\mathbb{C} P^ m\) has zero mean value when restricted to \(M\), then the submanifold \(M\) is full.