Classification of minimal surfaces in $S^5$ with constant contact angle

Geometry Topology Seminar
Monday, October 8, 2012 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 006
Rodrigo Montes – Univerity of Curitiba, Brazil –
Mohammad Ghomi
In this talk we introduce the notions of the contact angle and of the holomorphic angle for immersed surfaces in $S^{2n+1}$. We deduce formulas for the Laplacian and for the Gaussian curvature, and we will classify minimal surfaces in $S^5$ with the two angles constant. This classification gives a 2-parameter family of minimal flat tori of $S^5$. Also, we will give an alternative proof of the classification of minimal Legendrian surfaces in $S^5$ with constant Gaussian curvature. Finally, we will show some remarks and generalizations of this classification.