Translation and homothetical surfaces in Euclidean space with constant curvature

Rafael Lopez , Marilena Moruz (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.

Mots clés: Gauss curvature; Homothetical surface; Mean curvature; Translation surface

Domaines: Mathématiques [math]

Rafael Lopez, Marilena Moruz. Translation and homothetical surfaces in Euclidean space with constant curvature. Journal of the Korean Mathematical Society, 2014, 52 (3), pp.523-535. ⟨10.4134/JKMS.2015.52.3.523⟩. ⟨hal-03172983⟩