The Gauss map and second fundamental form of surfaces in a Lie group (Q325957)

In the paper under review, the integrability conditions for the existence of an isometric immersion from an orientable simply connected surface having prescribed Gauss map and positive extrinsic curvature into some unimodular Lie groups are given. It is shown that a surface isometrically immersed in the Euclidean unit sphere \(\mathbb{S}^{3}\) has positive constant extrinsic curvature if and only if its Gauss map is a harmonic map into the Riemann sphere.