Embedding Compact Riemann Surfaces in 4-dimensional Riemannian Manifolds

• Autores: Seokku Ko
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 2, 2005, págs. 355-366
• Idioma: inglés
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• Resumen

  • Any compact Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we prove that, given any compact Riemann surface S0, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. A model can be constructed by deforming a given topologically equivalent complete Riemann surface S in the normal direction NS of S. This result along with previous Ko Embedding theorem(see "Embedding compact Riemann surfaces in Riemannian Manifolds", Houston Journal of Mathematics, Vol. 27. no. 3, 2001) now shows that a compact Riemann surface admits conformal models in any Riemannian manifold of dimension greater than or equal to 3.