 
Summary: Bumpy 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
Revised Version
Abstract
The purpose of this article is to study conformal harmonic maps f :
M, where is a closed Riemann surface and M is a compact Rieman
nian manifold of dimension at least four. Such maps define parametrized
minimal surfaces, possibly with branch points. We show that when the
ambient manifold M is given a generic metric, all prime closed parametrized
minimal surfaces are free of branch points, and are as Morse nondegen
erate as allowed by the group of complex automorphisms of . They are
Morse nondegenerate in the usual sense if has genus at least two, lie on
twodimensional nondegenerate critical submanifolds if has genus one,
and on sixdimensional nondegenerate critical submanifolds if has genus
zero.
