Transactions of the American Mathematical Society

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

Author(s): Sebastián Montiel; Francisco Urbano
Journal: Trans. Amer. Math. Soc. 349 (1997), 2253-2269.
MSC (1991): Primary 53A10; Secondary 49Q20
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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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Sebastián Montiel
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain
Email: smontiel@goliat.ugr.es

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