Integrable deformation of critical surfaces in spaceforms (Q354707)

The author investigates a Goursat-type transformation for Bryant surfaces and a few of its geometric features. He proves that, when regarded as a non-isometric group action on the moduli space of CMC1 immersions of a fixed surface, the Lawson correspondence is equivariant with respect to the Goursat transform on minimal immersions. As particular cases one refinds certain well-known deformations of critical surfaces. Also he enlarges the number of explicitly computable cousin pairs, which are visualized in a quaternionic upper-half space.