Helicoidal surfaces with Δ ᴶ ᵣ = Ar in 3-dimensional Euclidean space
Keywords:
Surfaces of coordinate finite type, helicoidal surfaces, Laplace operator.Abstract
In this paper we study the helicoidal surfaces in the 3-dimensional Euclidean space under the condition ΔJ r = Ar; J = I; II; III; where A = (aij) is a constant 3 χ 3 matrix and ΔJ denotes the Laplace operator with respect to the fundamental forms I, II and III.
Mathematics Subject Classification (2010): 53A05, 53A07, 53C40.
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