Displaying similar documents to “Minimal surfaces in pseudohermitian geometry”

Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the ( 2 , 3 ) case

Nataliya Shcherbakova (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2 -dimensional surfaces in contact manifolds of dimension 3 . We show that in this case minimal surfaces are projections of a special class of 2 -dimensional...

On superminimal surfaces

Thomas Friedrich (1997)

Archivum Mathematicum

Similarity:

Using the Cartan method O. Boruvka (see [B1], [B2]) studied superminimal surfaces in four-dimensional space forms. In particular, he described locally the family of all superminimal surfaces and classified all of them with a constant radius of the indicatrix. We discuss the mentioned results from the point of view of the twistor theory, providing some new proofs. It turns out that the superminimal surfaces investigated by geometers at the beginning of this century as well...