Degree 3 algebraic minimal surfaces in the 3-sphere

Details Degree 3 algebraic minimal surfaces in the 3-sphere Degree 3 algebraic minimal surfaces in the 3-sphere

2011-08-23

arxiv.org/abs/1108.4463v1

Mathematics

Differential Geometry

19 pages

Scientific paper

We give a local analytic characterization that a minimal surface in the
3-sphere $\, \ES^3 \subset \R^4$ defined by an irreducible cubic polynomial is
one of the Lawson's minimal tori. This provides an alternative proof of the
result by Perdomo (\emph{Characterization of order 3 algebraic immersed minimal
surfaces of $S^3$},Geom. Dedicata 129 (2007), 23--34).

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