On stable compact minimal submanifolds
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- by Francisco Torralbo and Francisco Urbano PDF
- Proc. Amer. Math. Soc. 142 (2014), 651-658 Request permission
Abstract:
Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the stable compact minimal submanifolds of the product of two spheres is obtained. Also, it is proved that the only stable compact minimal surfaces of the product of a $2$-sphere and any Riemann surface are the complex ones.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): December 3, 2010
- Received by editor(s) in revised form: March 20, 2012
- Published electronically: October 25, 2013
- Additional Notes: This research was partially supported by MEyC-Feder research projects MTM2007-61775, MTM2011-22547 and the Junta Andalucía Grants P06-FQM-01642 and P09-FQM-4496.
- Communicated by: Michael Wolf
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 651-658
- MSC (2010): Primary 53C40, 53C42
- DOI: https://doi.org/10.1090/S0002-9939-2013-11810-1
- MathSciNet review: 3134005