A Remark on Compact Minimal Surfaces in $S^5$ with Non-Negative Gaussian Curvature
In this paper we classify compact minimal surfaces in $S^5$ with non-negative Gaussian curvature using the notion of a contact angle.
math.DG↗
arXiv subjects
Rodrigo Ristow Montes
Publications and source records attributed to Rodrigo Ristow Montes.
A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant Contact Angle
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.
math.DG↗
A Characterization of Minimal Surfaces in $S^5$ with Parallel Normal Vector Field
In this paper we proof that the Holomorphic angle for compact minimal surfaces in the sphere $S^5$ with constant Contact angle and with a parallel normal vector field must be constant.
math.DG↗
Contact Angle for Immersed Surfaces in $S^{2n+1}$
In this paper we introduce the notion of contact angle. We deduce formulas for Laplacian and Gaussian curvature of a minimal surface in $S^{2n+1}$ and give a characterization of the generalized Clifford Torus as the only non-legendrian minimal surface in $S^5$ with constant Contact and Kaehler angles.
math.DG↗