• Corpus ID: 126085370

# Surfaces minimales et la construction de Calabi-Penrose

@inproceedings{Blaine1984SurfacesME,
title={Surfaces minimales et la construction de Calabi-Penrose},
author={Harold A. Blaine and J. S. Lawson},
year={1984}
}
• Published 1984
• Mathematics
© Société mathématique de France, 1985, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Twisteurs et applications harmoniques en dimension 4
© Séminaire de Théorie spectrale et géométrie (Chambéry-Grenoble), 1985-1986, tous droits réservés. L’accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l’accord
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## References

SHOWING 1-9 OF 9 REFERENCES
Self-duality in four-dimensional Riemannian geometry
• Mathematics
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
• 1978
We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual
STORA - Regular solutions of the CPn models and further generalizations
• CERN preprint,
• 1980
LAWSON, Jr. - Calibrated Geometries
• Acta Math
• 1982
S.U.N.Y. Department of rlathematics STONY BROOK - NY
• 1982
ZAKRZEWSKI - General classical solutions in the CPn-1 model, Nucl
• Phys. B
• 1980
Wiley-Interscience
• New York,
• 1978
CHERN - On minimal spheres in the 4-sphere, Studies and essays presented to T.W
• 1970