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Self-intersections of Closed Parametrized Minimal Surfaces in Generic Riemannian Manifolds
 

Summary: Self-intersections of Closed Parametrized Minimal
Surfaces in Generic Riemannian Manifolds
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
e-mail: moore@math.ucsb.edu
Abstract
This article shows that for a generic choice of Riemannian metric on
a compact manifold M of dimension at least five, all prime compact
parametrized minimal surfaces within M are imbeddings. Moreover, if
M has dimension four, all prime compact parametrized minimal surfaces
within M have transversal self-interstions, and at any self-intersection the
tangent planes fail to be complex for any choice of orthogonal complex
structure in the tangent space.
1 Introduction
This article presents an application of the bumpy metric theorem for compact
parametrized minimal surfaces in Riemannian manifolds which was established
in an earlier article [4]. We will show that if M has dimension at least four, then
for generic choice of Riemannian metric on M, all prime compact parametrized

  

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

 

Collections: Mathematics