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In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb E^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb E^4_1$.
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참고문헌 (21)
참고문헌 신청
B.-Y. Chen / 1984 / Total Mean Curvature and Submanifolds of Finite Type / World Scientific
B.-Y. Chen / 1987 / Submanifolds with finite type Gauss map / Bull. Aust. Math. Soc 35 (2) : 161 ~ 186
Bang-Yen Chen / 2005 / SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP / 대한수학회지 42 (3) : 447 ~ 455
C. L. E. Moore / 1919 / Surfaces of rotation in a space of four dimensions / Ann. Math 21 (2) : 81 ~ 93
F. N. Cole / 1890 / On rotations in space of four dimensions / Amer. J. Math 12 (2) : 191 ~ 210
B.-Y. Chen / 1987 / Submanifolds with finite type Gauss map / Bull. Aust. Math. Soc 35 (2) : 161 ~ 186
Bang-Yen Chen / 2005 / SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP / 대한수학회지 42 (3) : 447 ~ 455
C. L. E. Moore / 1919 / Surfaces of rotation in a space of four dimensions / Ann. Math 21 (2) : 81 ~ 93
F. N. Cole / 1890 / On rotations in space of four dimensions / Amer. J. Math 12 (2) : 191 ~ 210
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