| Abstrakt: |
A Ricci surface is defined to be a Riemannian surface (M , g M) whose Gauss curvature K satisfies the differential equation K Δ K + g M d K , d K + 4 K 3 = 0 . In the case where K < 0 , this equation is equivalent to the well-known Ricci condition for the existence of minimal immersions in R 3 . Recently, Andrei Moroianu and Sergiu Moroianu proved that a Ricci surface with non-positive Gauss curvature admits locally an isometric minimal immersion into R 3 . In this paper, we are interested in studying non-compact orientable Ricci surfaces with non-positive Gauss curvature. Firstly, we give a definition of catenoidal end for non-positively curved Ricci surfaces. Secondly, we develop a tool which can be regarded as an analogue of the Weierstrass data to obtain some classification results for non-positively curved Ricci surfaces of genus zero with catenoidal ends. Furthermore, we also give an existence result for non-positively curved Ricci surfaces of arbitrary positive genus which have finite catenoidal ends. [ABSTRACT FROM AUTHOR] |
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