On Some Weingarten Surfaces in the Special Linear Group SL(2,R)

Abstract

We classify Weingarten conoids in the real special linear group SL(2,R). In particular, there is no linear Weingarten nontrivial conoids in SL(2,R). We also prove that the only conoids in SL(2,R) with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant under left translations of the subgroup N is a Weingarten surface.