Translation-like Apollonius and Triangular Surfaces in Non-constant Curvature Thurston Geometries

Abstract In the present paper, we deal with non-constant curvature Thurston geometries [1–4]. We define and determine the generalized translation-like Apollonius surfaces and thus also bisector surfaces as a special case. Moreover, we give a possible definition of the “surface of a translation-like triangle” in each investigated geometry. In our work, we will use the projective model of Thurston geometries described by E. Molnár in [1].