Linear Weingarten factorable surfaces in isotropic spaces

Muhittin Evren Aydin, Alper Osman Ogrenmis
2017 Studia Universitatis Babes-Bolyai Matematica  
In this paper, we deal with the linear Weingarten factorable surfaces in the isotropic 3-space I^3 satisfying the relation aK+bH=c, where K is the relative curvature and H the isotropic mean curvature, a,b,cR. We obtain a complete classification for such surfaces in I^3. As a further study, we classify all graph surfaces in I^3 satisfying the relation K=H^2, which is the equality case of the famous Euler inequality for surfaces in a Euclidean space.
doi:10.24193/subbmath.2017.2.11 fatcat:my3edzecsrcm5dhghnl6wzb7ta