Ricci surfaces

• Andrei Moroianu ^[1] ; Sergiu Moroianu ^[2]
  1. [1] Université de Versailles-St Quentin, France
  2. [2] Institutul de Matematica al Academiei Române, Romania
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 4, 2015, págs. 1093-1118
• Idioma: inglés
• Enlaces
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• Resumen

  • A Ricci surface is a Riemannian 2-manifold (M, g) whose Gaussian curvature K satisfies K Δ K + g(dK, dK) + 4K3 = 0. Every minimal surface isometrically embedded in R3 is a Ricci surface of non-positive curvature.

    At the end of the 19th century Ricci-Curbastro has proved that, conversely, every point x of a Ricci surface has a neighborhood which embeds isometrically in R3 as a minimal surface, provided K(x) < 0. We prove this result in full generality by showing that Ricci surfaces can be locally isometrically embedded either minimally in R3 or maximally in R2,1, including near points of vanishing curvature. We then develop the theory of closed Ricci surfaces, possibly with conical singularities, and construct classes of examples in all genera g ≥ 2.