To Specify Surfaces of Revolution with Pointwise 1-type Gauss Map in 3-dimensional Minkowski Space

In this paper, by the studying of the Gauss map, Laplacian operator, curvatures of surfaces in R 1 and Bour’s theorem, we are going to identify surfaces of revolution with pointwise 1-type Gauss map property in 3−dimensional Minkowski space. Introduction The classification of submanifolds in Euclidean and Non-Euclidean spaces is one of the interesting topics in differential geometry and in this way one can find some attempts in terms of finite type submanifolds [1, 2, 3, 4, 5]. On the other hand Kobayashi in [8] classified space-like ruled minimal surfaces in R31 and its extension to the Lorentz version is done by de Woestijne in [11]. In continue, people encounter with the following problem: Classify all surfaces in 3-dimensional Minkowski space satisfying the pointwise 1-type Gauss map condition ∆N = kN for the Gauss map N and some function k. In 2000, D.W.Yoon and Y.H.Kim in [9] classified minimal ruled surfaces in terms of pointwise 1-type Gauss map in R31. On suitability oriented surface M in R with positive Gaussian curvature K, one can induce a positive definite second fundamental form II with component functions e, f , g. The second Gaussian curvature is defined by