On the Gauss map of surfaces of revolution without parabolic points
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In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map G satisfies the condition △^hG = AG,A∈Mat(3,R), where △^h denotes the Laplace operator of the second fundamental form h of the surface and Mat(3,R) the set of 3×3-real matrices, and also obtain the complete classification theorem for those. In particular, we have a characterization of an ordinary sphere in terms of it.
Abstract
In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map G satisfies the condition △^hG = AG,A∈Mat(3,R), where △^h denotes the Laplace operator of the second fundamental form h of the surface and Mat(3,R) the set of 3×3-real matrices, and also obtain the complete classification theorem for those. In particular, we have a characterization of an ordinary sphere in terms of it.
참고문헌 (16)
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