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

Summary: Nondegeneracy of Coverings of Minimal Tori and
Klein Bottles in Riemannian Manifolds
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
e-mail: moore@math.ucsb.edu
Abstract
We say that a parametrized minimal torus or Klein bottle in a ambient
Riemannian manifold M is Morse nondegenerate if it lies on a nondegener-
ate 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 bot-
tles 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.
1 Introduction
Suppose that Map(, M) is a suitable completion of the space of smooth maps
f : M from a compact connected surface into a Riemannian manifold M

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics