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In this paper, we classify translation surfaces in the three dimensional Galilean space $\mathbb{G}_{3}$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the second fundamental form of the surface. We also give explicit forms of these surfaces.
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참고문헌 (16)
참고문헌 신청
L. J. Alias / 1992 / Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying ∆x = Ax +B / Pacific J. Math 156(2):201~208
C. Baikoussis / 1993 / On the Gauss map of helicoidal surfaces / Rend. Sem. Math. Messina Ser. II 2(16):31~42
M. Bekkar / 2012 / Translation surfaces in the 3-dimensional space satisfying ∆IIIri = μiri / J. Geom 103(3):367~374
B. Y. Chen / 1996 / A report on submanifold of finite type / Soochow J. Math 22(2):117~337
S. M. Choi / 1995 / On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space / Tsukuba J. Math 19(2):351~367
C. Baikoussis / 1993 / On the Gauss map of helicoidal surfaces / Rend. Sem. Math. Messina Ser. II 2(16):31~42
M. Bekkar / 2012 / Translation surfaces in the 3-dimensional space satisfying ∆IIIri = μiri / J. Geom 103(3):367~374
B. Y. Chen / 1996 / A report on submanifold of finite type / Soochow J. Math 22(2):117~337
S. M. Choi / 1995 / On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space / Tsukuba J. Math 19(2):351~367
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