The Gauss maps of Demoulin surfaces with conformal coordinates

TL;DR

This paper studies Demoulin surfaces in real projective 3-space, establishing a generalized Weierstrass representation through primitive maps into a semi-Riemannian 6-symmetric space, advancing the understanding of their geometric structure.

Contribution

It introduces a novel Weierstrass type representation for definite Demoulin surfaces using primitive maps into a semi-Riemannian 6-symmetric space, expanding the theoretical framework.

Findings

Established a generalized Weierstrass representation for Demoulin surfaces.

Connected Demoulin surfaces with primitive maps into a semi-Riemannian 6-symmetric space.

Provided new insights into the geometry of Demoulin surfaces.

Abstract

Demoulin surfaces in real projective $3$-space are investigated. Our result enable us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian $6$-symmetric space.