Helicoidal surfaces in the three-dimensional Lorentz–Minkowski space satisfying ΔIIr_i = λ_ir_i

摘要

In this paper, we study helicoidal surfaces without parabolic points in the 3-dimensional Lorentz–Minkowski space under the condition ΔIIr_i = λiri where ΔII is the Laplace operator with respect to the second fundamental form and λ_i is a real number. We prove that there are no helicoidal surfaces without parabolic points in the 3-dimensional Lorentz–Minkowski space satisfying that condition.