Embedding open Riemann surfaces in 4-dimensional Riemannian manifolds
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 205-214
https://doi.org/10.4134/BKMS.2016.53.1.205
Printed January 31, 2016
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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