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

Montiel, Sebastián; Urbano, Francisco

doi:10.1090/S0002-9947-97-01933-8

Second variation of superminimal surfaces into self-dual Einstein four-manifolds
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by Sebastián Montiel and Francisco Urbano

Trans. Amer. Math. Soc. 349 (1997), 2253-2269

DOI: https://doi.org/10.1090/S0002-9947-97-01933-8

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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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