Abstract
In this paper we prove that any hypersurface in En+1 of the form 
where P
1 is a polynomial of degree ≥2 and P
2, ... , P
n are functions such that P
′
i
P
″
i
= 0 somewhere for all i = 2, ... , n, is of infinite type. As a consequence, we deduce that a polynomial translation hypersurface in En+1, i. e. a hypersurface of the above form where P
1, ... , P
n are polynomials, is of finite type if and only if it is a hyperplane. This provides some partial solutions to a problem of B. Y. Chen [C3].
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Dedicated to Professor Katsumi Nomizu on the occasion of his seventieth birthday
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Dillen, F., Verstraelen, L., Vrancken, L. et al. Classification of polynomial translation hypersurfaces of finite type. Results. Math. 27, 244–249 (1995). https://doi.org/10.1007/BF03322829
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DOI: https://doi.org/10.1007/BF03322829