Second Variation of Superminimal Surfaces into Self-dual Einstein Four-manifolds

@inproceedings{Montiel1997SecondVO,
  title={Second Variation of Superminimal Surfaces into Self-dual Einstein Four-manifolds},
  author={S. V{\'a}zquez y Montiel and Francisco Urbano},
  year={1997}
}
The index of a compact orientable superminimal surface of a selfdual 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 = S4 and M = CP2 are given, characterizing the standard Veronese immersions and their twistor deformations as those with lowest index.