Nondegeneracy of Coverings of Minimal Tori and Klein Bottles in Riemannian Manifolds

We say that a parametrized minimal torus or Klein bottle in a ambient Riemannian manifold M is Morse nondegenerate if it lies on a nondegenerate critical submanifold, which is also an orbit for the group of isometries of the flat metric of total area one. This article shows that for generic choice of Riemannian metric on a compact manifold M of dimension at least four, unbranched multiple covers of prime minimal tori or Klein bottles are Morse nondegenerate. A similar result is given for harmonic tori and Klein bottles. The proofs require a modification of techniques due to Bott for studying iterations of smooth closed geodesics.