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Bumpy Metrics and Closed Parametrized Minimal Surfaces in Riemannian Manifolds
 

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
e-mail: 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
two-dimensional nondegenerate critical submanifolds if has genus one,
and on six-dimensional nondegenerate critical submanifolds if has genus
zero.

  

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

 

Collections: Mathematics