 
Summary: Bumpy Riemannian Metrics and Closed
Parametrized Minimal Surfaces in Riemannian
Manifolds
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
email: moore@math.ucsb.edu
Abstract
This article is concerned with conformal harmonic maps f : M,
where is a closed Riemann surface and M is a compact Riemannian
manifold of dimension at least four. We show that when the ambient
manifold M is given a generic metric, all prime closed parametrized min
imal surfaces are free of branch points, and are as Morse nondegenerate
as allowed by the group of complex automorphisms of .
1 Introduction
This article is devoted to providing part of the foundation needed for a partial
Morse theory for parametrized minimal surfaces in Riemannian manifolds which
should parallel the wellknown Morse theory of smooth closed geodesics in a
compact Riemannian manifold M. Recall that the theory of closed geodesics is
