On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces
Keyword(s):
We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space $\mathbb {R}^{n+1},\,\;n\geq 2,$ defined by polynomials of odd degree. Also we prove that the hyperspheres and the round cylinders are the only regular algebraic hypersurfaces with non-zero constant mean curvature in $\mathbb {R}^{n+1}, n\geq 2,$ defined by polynomials of degree less than or equal to three. These results give partial answers to a question raised by Barbosa and do Carmo.
2019 ◽
Vol 16
(05)
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pp. 1950076
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Keyword(s):
1972 ◽
Vol 45
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pp. 139-165
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1982 ◽
Vol 17
(2)
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pp. 337-356
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Keyword(s):
2020 ◽
Vol 2020
(763)
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pp. 223-249
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