# EMBEDDING OPEN RIEMANN SURFACES IN 4-DIMENSIONAL RIEMANNIAN MANIFOLDS

• Published : 2016.01.31
• 58 6

#### 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

#### References

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