Conformally flat hypersurfaces in Euclidean 4-space
Keyword(s):
AbstractWe study generic and conformally flat hypersurfaces in Euclidean four-space. What kind of conformally flat three manifolds are really immersed generically and conformally in Euclidean space as hypersurfaces? According to the theorem due to Cartan [1], there exists an orthogonal curvature-line coordinate system at each point of such hypersurfaces. This fact is the first step of our study. We classify such hypersurfaces in terms of the first fundamental form. In this paper, we consider hypersurfaces with the first fundamental forms of certain specific types. Then, we give a precise representation of the first and the second fundamental forms of such hypersurfaces, and give exact shapes in Euclidean space of them.
A CLASSIFICATION AND A NON-EXISTENCE THEOREM FOR CONFORMALLY FLAT HYPERSURFACES IN EUCLIDEAN 4-SPACE
2005 ◽
Vol 16
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pp. 53-85
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2000 ◽
Vol 24
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pp. 43-48
2017 ◽
Vol 55
(1)
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pp. 87-98
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1973 ◽
Vol 25
(6)
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pp. 1170-1173
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1959 ◽
Vol 15
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pp. 201-217
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2006 ◽
Vol 30
(4)
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pp. 383-396
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2020 ◽
Vol 69
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pp. 101611