Resumen de Nondegeneracy of coverings of minimal tori and Klein bottles in Riemannian manifolds

John Douglas Moore

• We say that a parametrized minimal torus or Klein bottle in an ambient Riemannian manifold 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. We show that for a generic choice of a Riemannian metric on a compact manifold of dimension at least four, unbranched multiple covers of prime minimal tori or Klein bottles are Morse nondegenerate. A similar result holds for harmonic tori and Klein bottles. The proofs require a modification of techniques of Bott for studying iterations of smooth closed geodesics.