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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Gauss curvature of compact surfaces in homogeneous 3-manifolds


Authors: Francisco Torralbo and Francisco Urbano
Journal: Proc. Amer. Math. Soc. 138 (2010), 2561-2567
MSC (2010): Primary 53C42; Secondary 53C30
Published electronically: February 25, 2010
MathSciNet review: 2607886
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Abstract: Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Nonexistence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.


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Additional Information

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

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

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10316-5
PII: S 0002-9939(10)10316-5
Received by editor(s): March 12, 2009
Received by editor(s) in revised form: October 20, 2009
Published electronically: February 25, 2010
Additional Notes: This research was partially supported by MCyT-Feder research project MTM2007-61775 and Junta Andalucía Grant P06-FQM-01642.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2010 American Mathematical Society