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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 Cheng-Yau 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.
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참고문헌 (24)
참고문헌 신청
A. Ferrandez / 1992 / On surfaces in the 3-dimensional Lorentz-Minkowski space / Pacific J. Math 152 (1) : 93 ~ 100
B. Y. Chen / 1986 / Energy, tension and finite type maps / Kodai Math. J 9 (3) : 406 ~ 418
B. Y. Chen / 1987 / Submanifolds with finite type Gauss map / Bull. Austral. Math. Soc 35 (2) : 161 ~ 186
B. Y. Chen / 1991 / Some open problems and conjectures on submanifolds of finite type / Soochow J. Math 17 (2) : 169 ~ 188
B. Y. Chen / 1996 / A report on submanifolds of finite type / Soochow J. Math 22 (2) : 117 ~ 337
B. Y. Chen / 1986 / Energy, tension and finite type maps / Kodai Math. J 9 (3) : 406 ~ 418
B. Y. Chen / 1987 / Submanifolds with finite type Gauss map / Bull. Austral. Math. Soc 35 (2) : 161 ~ 186
B. Y. Chen / 1991 / Some open problems and conjectures on submanifolds of finite type / Soochow J. Math 17 (2) : 169 ~ 188
B. Y. Chen / 1996 / A report on submanifolds of finite type / Soochow J. Math 22 (2) : 117 ~ 337
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