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Finitely curved orbits of complex polynomial vector fields 42
Mafra,Albetã C..
This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?
Tipo: Info:eu-repo/semantics/article Palavras-chave: Holomorphic foliations; Polynomial vector fields; Algebraic curves; Finite total curvature.
Ano: 2007 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000100002
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The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature 42
HINOJOSA,PEDRO A.; SILVA,GILVANEIDE N..
In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature. We give a different proof of the following theorem of R. Osserman:The normal Gauss map of a minimal surface immersed inℝ3with finite total curvature, which is not a plane, omits at most three points of&#55349;&#56650;2Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2.
Tipo: Info:eu-repo/semantics/article Palavras-chave: Gauss map; Minimal surfaces; Finite total curvature; Image of the Gauss map.
Ano: 2013 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652013000401217
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