Annals of Global Analysis and Geometry

, Volume 12, Issue 1, pp 97–101 | Cite as

Linear structures on the collections of minimal surfaces in3 and4

  • Anthony J. Small


The collection of ‘minimal herissons’ in3 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 words

Minimal surface null holomorphic curve 

MSC 1991

53 C 42 14 E 05 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Anthony J. Small
    • 1
  1. 1.Department of Mathematics and Computer ScienceThe University DundeeScotland, U.K.

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