Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON POINTWISE 1-TYPE GAUSS MAP OF SURFACES IN 𝔼31 CONCERNING CHENG-YAU OPERATOR

  • Received : 2015.12.19
  • Published : 2017.03.01
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Abstract

In this paper, we study surfaces in 3-dimensional Minkowski space in terms of certain type of their Gauss map. We give several results on these surfaces whose Gauss map G satisfies ${\square}G=f(G+C)$ for a smooth function f and a constant vector C, where ${\square}$ denotes the ChengYau operator. In particular, we obtain classification theorems on the rotational surfaces in ${\mathbb{E}}^3_1$ with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.

Keywords

Acknowledgement

Grant : Y EUCL2TIP

Supported by : National Research Foundation of Korea (NRF), TUBITAK

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