On spectral geometry of minimal surfaces in 𝐂𝐏ⁿ

Abstract

By employing the standard isometric imbedding of C P n C{P^n} into the Euclidean space, a classification theorem for full, minimal, 2 2 -type surfaces in C P n C{P^n} that are not ± \pm holomorphic is given. All such compact minimal surfaces are either totally real minimal surfaces in C P 2 C{P^2} or totally real superminimal surfaces in C P 3 C{P^3} and C P 4 C{P^4} . In the latter case, they are locally unique. Moreover, some eigenvalue inequalities for compact minimal surfaces of C P n C{P^n} with constant Kaehler angle are shown.