Complete 3-dimensional 𝜆-translators in the Minkowski space ℝ⁴₁

Abstract

In this paper, we obtain the classification theorem for 3-dimensional complete space-like 𝜆-translators 𝑥 : 𝑀³ → ℝ⁴₁ with constant norm of the second fundamental form and constant 𝑓₄ = ∑_{𝑖,𝑗,𝑘,𝑙} ℎ_𝑖𝑗 ℎ_𝑗𝑘 ℎ_𝑘𝑙 ℎ_𝑙𝑖 with ℎ_𝑖𝑗 being the components of the second fundamental form in the Minkowski space ℝ⁴₁.