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http://dx.doi.org/10.4134/BKMS.2016.53.1.205

EMBEDDING OPEN RIEMANN SURFACES IN 4-DIMENSIONAL RIEMANNIAN MANIFOLDS

Ko, Seokku (School of Business Administration and Economics Konkuk University)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 205-214 More about this Journal

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;

Citations & Related Records

Reference

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