Families of flat minimal tori in \(\mathbb{C} P^ n\)
Infinite families of noncongruent, flat minimal tori are found in \(\mathbb{C} P^n\) for \(n\geq 3\). Continuous families of such tori are found when \(n\geq 5\). These examples are all weakly Lagrangian, but not, in general, contained in a unitary copy of \(\mathbb{R} P^n\subset \mathbb{C} P^n\). Among these minimal tori, some have a cyclic harmonic sequence while others have an infinite noncyclic harmonic sequence. It is shown that for a generic flat torus, there is no isometric, weakly Lagrangian harmonic map from it into \(\mathbb{C} P^n\). Infinite families of noncongruent, flat minimal tori are found in \(S^{2m+ 1}\) for \(m\geq 2\). Continuous families of such tori are found when \(m\geq 3\).
scientific article; zbMATH DE number 844215