Degree of the standard isometric minimal immersions of the symmetric spaces of rank one into spheres

Abstract

Let k : Sin+3->QPn be the Hopf fibration,where we consider Sin+3 as the unit sphere in Qn+l -C2n+2. Then for each eigen-function / on QPn which belongs to Vk, there exists a homogeneous harmonic polynomial Pf of type (k,k) on C2n+2 which induces / through n. So the degree of the immersion coincides with the algebraic degree of the homogeneous polynomials which define the immersion. Theorem B. Let Xk be the k-th standard isometric minimal immersion of the Cayley projective plane CayP2. Then Xk has degree 2k.