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EMBEDDING OPEN RIEMANN SURFACES IN 4-DIMENSIONAL RIEMANNIAN MANIFOLDS

  • Ko, Seokku (School of Business Administration and Economics Konkuk University)
  • Received : 2015.01.26
  • Published : 2016.01.31

Abstract

Any open Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we will prove that, given any open Riemann surface, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. This result along with [5] now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension ${\geq}3$.

Keywords

embedding open Riemann surface;4-dimensional Riemannian manifold;$Teichm{\ddot{u}}ller$ space;conformal deformation

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