Acta mathematica scientia, Series B >
DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE
We give a local analytic characterization that a minimal surface in the 3-sphere S3 ( R4 defined by an irreducible cubic polynomial is one of the Lawson´s minimal tori. This provides an alternative proof of the result by Perdomo (Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 (2007), 23–34).
Key words： algebraic minimal surface; 3-sphere; cubic polynomial
Joe S. Wang . DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE[J]. Acta mathematica scientia, Series B, 2012 , 32(6) : 2065 -2084 . DOI: 10.1016/S0252-9602(12)60160-X
[1] Hsiang Wu-yi. Remarks on closed minimal submanifolds in the standard Riemannian m-sphere. J Differ-ential Geometry, 1967, 1: 257–267
[2] Hsiang Wu-yi, Lawson B. Minimal submanifolds of low cohomogeneity. J Differential Geometry, 1971, 5: 1–38
[3] Lawson B. Complete minimal surfaces in S3. Ann Math, 1970, 92(2): 335–374
[4] Perdomo O M. Characterization of order 3 algebraic immersed minimal surfaces of S3. Geom Dedicata, 2007, 129: 23–34
[5] Yamada K. Minimal tori in S3 whose lines of curvature lie in S2. Tokyo J Math, 1987, 10: 215–226
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