On C-totally real submanifolds of S^2n+1 (1) with non-negative sectional curvature

For all n 4, we give a complete classification of the compact n-dimensional minimal C-totally real submanifolds in the (2n+1) -dimensional unit sphere S^2n+1 (1) with non-negative sectional curvature. This generalizes the results of Yamaguchi et al (Proc Amer Math Soc 54: 276-280, 1976) for n = 2 and, Dillen and Vrancken (Math J Okayama Univ 31: 227-242, 1989) for n = 3. Additionally, we show that, as compact minimal C-totally real submanifolds, the standard embeddings of the symmetric spaces SU (m) /SO (m), SU (m), SU (2m) /Sp (m) for each m 3, and E₆/F₄ into S^2n+1 (1) are all Willmore submanifolds, with n=12m (m-1) -1, m²-1, 2m²-m-1 and 26, respectively.