On the Gauss curvature of compact surfaces in homogeneous 3-manifolds
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- by Francisco Torralbo and Francisco Urbano PDF
- Proc. Amer. Math. Soc. 138 (2010), 2561-2567 Request permission
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.References
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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
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2561-2567
- MSC (2010): Primary 53C42; Secondary 53C30
- DOI: https://doi.org/10.1090/S0002-9939-10-10316-5
- MathSciNet review: 2607886