A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant Contact Angle

Details A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant Contact Angle A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant Contact Angle

2006-11-28

arxiv.org/abs/math/0611888v1

Mathematics

Differential Geometry

9 pages

Scientific paper

We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we will give a characterization of flat minimal surfaces in $S^5$ with constant contact angle.

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