On translation surfaces of framed curves

Abstract

Abstract In this study, we study translation surfaces of framed curves in the 3-dimensional Euclidean space E3. First, we compute some important equations and geometric invariants such as first and second fundamental forms, Gauss equations, Christoffel symbols, Mainardi-Codazzi equations and Egregium Theorema. Using these equations, we introduce some characterizations of translation surfaces of framed curves. Also, we study some special cases such as framed generating curves of the surface are framed Bertrand-partner curves or Mannheim-partner curves. MSC: 53A04, 53A05, 53A55.