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 M97, S, Sz22-3,W06. We define and determine the generalized trans\-lation-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. Moln\'ar in M97.
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