SURFACES OF REVOLUTION SATISFYING △IIG = f(G + C)
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In this paper, we study surfaces of revolution without par- abolic points in 3-Euclidean space R3, satisfying the condition △IIG = f(G+ C), where △II is the Laplace operator with respect to the second fundamental form, f is a smooth function on the surface and C is a con- stant vector. Our main results state that surfaces of revolution without parabolic points in R3 which satisfy the condition △IIG = fG, coincide with surfaces of revolution with non-zero constant Gaussian curvature.
Abstract
In this paper, we study surfaces of revolution without par- abolic points in 3-Euclidean space R3, satisfying the condition △IIG = f(G+ C), where △II is the Laplace operator with respect to the second fundamental form, f is a smooth function on the surface and C is a con- stant vector. Our main results state that surfaces of revolution without parabolic points in R3 which satisfy the condition △IIG = fG, coincide with surfaces of revolution with non-zero constant Gaussian curvature.
참고문헌 (16)
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