Minimal immersions of projective spaces into spheres (Q1073362)

The author estimates from below the dimension of the parameter space of equivalence classes of full isometric minimal immersions into spheres of \((P^ n{\mathbb{C}}\), \(\lambda_ k/2n g)\), \(n\geq 2\) and \(k\geq 4\), and \((P^ 2{\mathbb{H}},(\lambda_ k/8)g)\), \(k\geq 4\), where \(\lambda_ k\) is the k-th eigenvalue of the Laplacian. In particular, it follows that these immersions are not rigid since the dimensions are positive. The same problem for minimal immersions of spheres into spheres was solved by \textit{M. do Carmo} and \textit{N. Wallach} [Ann. Math., II. Ser. 93, 43-62 (1971; Zbl 0218.53069)].