Eigenmaps and minimal immersions of projective spaces into spheres
In [Ann. Math., II. Ser. 93, 43-62 (1971; Zbl 0218.53069)] \textit{M. P. do Carmo} and \textit{N. R. Wallach} showed that the set of equivalence classes of full isometric minimal immersions of a compact symmetric space M into a sphere can be parameterized by a convex body in a vector space \(L_ M\). Similarly, \textit{G. Toth} and \textit{G. d'Ambra} showed in [Geom. Dedicata 17, 61-67 (1984; Zbl 0551.58013)] that equivalence classes of full eigenmaps of M into a sphere can be parameterized by a convex body in a vector space \(L_ E\). The author estimates the dimension of \(L_ M\) and \(L_ E\) from below when M is a quaternionic projective space or the Cayley plane. This was done for complex projective spaces by \textit{H. Urakawa} in [Tsukuba J. Math. 9, 321-347 (1985; Zbl 0588.53041)].
scientific article; zbMATH DE number 4058352
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