Linear structures on the collections of minimal surfaces inℝ3 andℝ4
- 25 Downloads
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
Unable to display preview. Download preview PDF.
- Griffiths, P.;Harris, J.:Principles of Algebraic Geometry. Wiley-Intersience, 1978.Google Scholar
- Hartshorne, R.:Algebraic Geometry. Springer-Verlag, 1977.Google Scholar
- Hoffman, D.A.;Osserman, R.:The Geometry of the Generalized Gauss Map. Memoir of the AMS, vol. 28 no. 236 (1980).Google Scholar
- Lawson, H.B.:Lectures on Minimal Submanifolds. Volume 1. Publish or Perish, 1980.Google Scholar
- Ossermann, R.:A Survey of Minimal Surfaces. Dover, 1986.Google Scholar
- Rosenberg, H.;Toubiana, E.: Complete minimal surfaces and minimal herissons.J. Differential Geom. 28 (1988), 115–132.Google Scholar
- Small, A.J.: Minimal surfaces in ℝ3 and algebraic curves.Diff. Geom. Appl. 2 (1992), 369–384.Google Scholar
- Small, A.J.:Minimal surfaces in ℝ 4 and the Klein correspondence. In preparation.Google Scholar
- Small, A.J.:Duality for Calabi curves and minimal surfaces in ℝ n. MPI 92-61 (1992).Google Scholar