Abstract
We show that the only quadrics of finite type in Euclidean 3-space are the circular cylinder and the sphere.
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References
B.-Y. Chen, “Total mean curvature and submanifolds of finite type,” World Scientific, Singapore, 1984.
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B.-Y. Chen, F. Dillen, L. Verstraelen, L. Vrancken,Ruled surfaces of finite type, Bull. Austr. Math. Soc. (to appear)
O. Garay,Finite type cones shaped on spherical submanifolds, Proc. Amer. Mat. Soc.104 (1988), 868–870.
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This work was done while the second author was visiting the Michigan State University. He would like to thank MSU, and in particular the staff of the department of mathematics for their hospitality.
Research Assistant of the National Fund for Scientific Research (Belgium)
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Chen, BY., Dillen, F. Quadrics of finite type. J Geom 38, 16–22 (1990). https://doi.org/10.1007/BF01222891
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DOI: https://doi.org/10.1007/BF01222891