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We study the Gauss map G of ruled surfaces in the 3-dim- ensional Euclidean space E3 with respect to the so called Cheng-Yau operator □ acting on the functions defined on the surfaces. As a result, we establish the classification theorem that the only ruled surfaces with Gauss map G satisfying □G = AG for some 3 × 3 matrix A are the flat ones. Furthermore, we show that the only ruled surfaces with Gauss map G satisfying □G = AG for some nonzero 3×3 matrix A are the cylindrical surfaces.
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참고문헌 (26)
참고문헌 신청
B.-Y. Chen / 1984 / Total Mean Curvature and Submanifolds of Finite Type / World Scientific Publ
B.-Y. Chen / 1985 / Finite Type Submanifolds and Generalizations / University of Rome
B.-Y. Chen / 1987 / Submanifolds with finite type Gauss map / Bull. Austral. Math. Soc 35 (2) : 161 ~ 186
C. Baikoussis / 1992 / On the Gauss map of ruled surfaces / Glasgow Math. J 34 (3) : 355 ~ 359
C. Baikoussis / 1993 / On the Gauss map of helicoidal surfaces / Rend. Sem. Mat. Messina Ser. II 2 (16) : 31 ~ 42
B.-Y. Chen / 1985 / Finite Type Submanifolds and Generalizations / University of Rome
B.-Y. Chen / 1987 / Submanifolds with finite type Gauss map / Bull. Austral. Math. Soc 35 (2) : 161 ~ 186
C. Baikoussis / 1992 / On the Gauss map of ruled surfaces / Glasgow Math. J 34 (3) : 355 ~ 359
C. Baikoussis / 1993 / On the Gauss map of helicoidal surfaces / Rend. Sem. Mat. Messina Ser. II 2 (16) : 31 ~ 42
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