Abstract
The collection of ‘minimal herissons’ inℝ 3 is endowed with a vector space structure. The existence of this structure is related to the fact that null curves inC 3 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 inC 4. This gives a similar class of minimal surfaces in ℝ4.
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Small, A.J. Linear structures on the collections of minimal surfaces inℝ 3 andℝ 4 . Ann Glob Anal Geom 12, 97–101 (1994). https://doi.org/10.1007/BF02108290
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DOI: https://doi.org/10.1007/BF02108290