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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Second variation of superminimal surfaces into self-dual Einstein four-manifolds


Authors: Sebastián Montiel and Francisco Urbano
Journal: Trans. Amer. Math. Soc. 349 (1997), 2253-2269
MSC (1991): Primary 53A10; Secondary 49Q20
MathSciNet review: 1422905
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Abstract: The index of a compact orientable superminimal surface of a self-dual Einstein four-manifold $M$ with positive scalar curvature is computed in terms of its genus and area. Also a lower bound of its nullity is obtained. Applications to the cases $M=\mathbb {S}^4$ and $M=\mathbb {C}\mathbb {P}^2$ are given, characterizing the standard Veronese immersions and their twistor deformations as those with lowest index.


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Additional Information

Sebastián Montiel
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain
Email: smontiel@goliat.ugr.es

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

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01933-8
PII: S 0002-9947(97)01933-8
Keywords: Superminimal surfaces, index, nullity
Received by editor(s): October 10, 1994
Received by editor(s) in revised form: September 15, 1995
Additional Notes: Both authors partially supported by DGICYT grant PB94–0796
Article copyright: © Copyright 1997 American Mathematical Society