Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(1): 205-214

Printed January 31, 2016

https://doi.org/10.4134/BKMS.2016.53.1.205

Copyright © The Korean Mathematical Society.

Embedding open Riemann surfaces in 4-dimensional Riemannian manifolds

Seokku Ko

Konkuk University

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 \cite{ko6} now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension $\ge 3.$

Keywords: embedding open Riemann surface, 4-dimensional Riemannian manifold, Teichm\"{u}ller space, conformal deformation

MSC numbers: 30F60

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