The Gauss map for Lagrangean and isoclinic surfaces

TL;DR

This paper explores how the Gauss map characterizes key classes of surfaces in Euclidean space, including Lagrangean and isoclinic surfaces, revealing simple properties that distinguish these classes.

Contribution

It introduces simple properties of the Gauss map that characterize Lagrangean and isoclinic surfaces in Euclidean space.

Findings

Characterization of R-surfaces via the Gauss map

Identification of properties distinguishing Lagrangean surfaces

Identification of properties distinguishing isoclinic surfaces

Abstract

Simple properties of the Gauss map characterise important classes of surfaces in $\Rq$: $R$-surfaces, the real version of plane complex curves; Lagrangean surfaces; isoclinic surfaces.