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

• Autores: John Douglas Moore
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 230, Nº 1, 2007, págs. 147-166
• Idioma: inglés
• DOI: 10.2140/pjm.2007.230.147
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• Resumen

  • 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.