Mappings of moduli spaces for harmonic eigenmaps and minimal immersions between spheres (Q1203590)

It is known that the space of equivalence classes of full \(\lambda_ p\)- eigenmaps \(f: S^ m \to S_ V\) can be parametrized by its moduli space \({\mathcal L}_{\lambda_ p}\), where \(\lambda_ p\) is the \(p\)-th eigenvalue of the Laplace-Beltrami operator on the Euclidean \(m\)-sphere \(S^ m\), \(m \geq 2\). The classification of \(\lambda_ p\)-eigenmaps is equivalent to describing \({\mathcal L}_{\lambda_ p}\). The author proves that \({\mathcal L}_{\lambda_ p}\) can be equivariantly imbedded into \({\mathcal L}_{\lambda_{p+1}}\), and thereby gives new examples of \(\lambda_ p\)-eigenmaps for higher values of \(p\). The case of minimal immersions is also studied.