Willmore Surfaces of ?4 and the Whitney Sphere |
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| Authors: | Ildefonso Castro and Francisco Urbano |
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| Institution: | (1) Departamento de Matemáticas Escuela Politécnica Superior, Universidad de Jaén, 23071 Jaén, Spain;(2) Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain. e-mail |
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| Abstract: | We make a contribution to the study of Willmore surfaces infour-dimensional Euclidean space  4 by making useof the identification of 4 with two-dimensionalcomplex Euclidean space  2. We prove that theWhitney sphere is the only Willmore Lagrangian surface of genus zero in4 and establish some existence and uniquenessresults about Willmore Lagrangian tori in 4 2. |
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| Keywords: | Lagrangian surfaces Whitney sphere Willmore tori |
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