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

Geometry Topology Seminar
Monday, October 8, 2012 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Univerity of Curitiba, Brazil
 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.