## Abstract

In this paper, we study surfaces in E^{3} whose Gauss map G satisfies the equation □ G = f(G + C) for a smooth function f and a constant vector C, where □ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation □G = λ(G + C) for a constant λ and a constant vector C.

Original language | English |
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Pages (from-to) | 935-949 |

Number of pages | 15 |

Journal | Bulletin of the Korean Mathematical Society |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

## Keywords

- □-pointwise 1-type
- Cheng-Yau operator
- Gauss map

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