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July, 2016 Constant mean curvature proper-biharmonic surfaces of constant Gaussian curvature in spheres
Eric LOUBEAU, Cezar ONICIUC
J. Math. Soc. Japan 68(3): 997-1024 (July, 2016). DOI: 10.2969/jmsj/06830997

Abstract

Constant mean curvature (CMC) surfaces in spheres are investigated under the extra condition of biharmonicity. From the work of Miyata, especially in the flat case, we give a complete description of such immersions and show that for any $h \in (0,1)$ there exist CMC proper-biharmonic planes and cylinders in ${\mathbb S}^5$ with $|H|=h$, while a necessary and sufficient condition on $h$ is found for the existence of CMC proper-biharmonic tori in ${\mathbb S}^5$.

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Eric LOUBEAU. Cezar ONICIUC. "Constant mean curvature proper-biharmonic surfaces of constant Gaussian curvature in spheres." J. Math. Soc. Japan 68 (3) 997 - 1024, July, 2016. https://doi.org/10.2969/jmsj/06830997

Information

Published: July, 2016
First available in Project Euclid: 19 July 2016

zbMATH: 06642401
MathSciNet: MR3523535
Digital Object Identifier: 10.2969/jmsj/06830997

Subjects:
Primary: 53C42
Secondary: 53C43 , 58E20

Keywords: biharmonic map , Constant mean curvature surfaces

Rights: Copyright © 2016 Mathematical Society of Japan

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Vol.68 • No. 3 • July, 2016
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