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A characterization of the Lagrangian pseudosphere

Author(s): Ildefonso Castro; Francisco Urbano
Journal: Proc. Amer. Math. Soc. 132 (2004), 1797-1804.
MSC (2000): Primary 53C42, 53B25; Secondary 53A05, 53D12
Posted: December 31, 2003
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Abstract | References | Similar articles | Additional information

Abstract: We characterize the Lagrangian pseudosphere as the only branched Lagrangian immersion of a sphere in complex Euclidean plane with constant length mean curvature vector.

References:

1.: B. Y. Chen, Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tôhoku Math. J. 49 (1997), 277-297. MR 98g:53096
2.: R. Gulliver, R. Osserman and H. Royden, A theory of branched immersions of surfaces, Amer. J. Math. 95 (1973), 750-812. MR 50:14595

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Additional Information:

Ildefonso Castro
Affiliation: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Jaén, 23071 Jaén, Spain
Email: icastro@ujaen.es

Francisco Urbano
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: furbano@ugr.es

DOI: 10.1090/S0002-9939-03-07377-5
PII: S 0002-9939(03)07377-5
Keywords: Constant length mean curvature vector, Lagrangian surfaces
Received by editor(s): February 11, 2003
Posted: December 31, 2003
Additional Notes: Research partially supported by an MCYT and FEDER grant BFM2001-2967
Dedicated: Dedicated to B. Y. Chen on his 60th birthday
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2003, American Mathematical Society


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