Linear structures on the collections of minimal surfaces inℝ3 andℝ4
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The collection of ‘minimal herissons’ inℝ3 is endowed with a vector space structure. The existence of this structure is related to the fact that null curves inC3 are described by a single map from the étalé space of the sheaf of germs of holomorphic sections of the line bundle of degree 2 over ℙ1 to C3, which islinear on stalks. There is an analogous construction for null curves inC4. This gives a similar class of minimal surfaces in ℝ4.
Key wordsMinimal surface null holomorphic curve
MSC 199153 C 42 14 E 05
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