Special Lagrangian m-folds in ℂ m with symmetries
Joyce, Dominic
Duke Math. J., Tome 115 (2002) no. 1, p. 1-51 / Harvested from Project Euclid
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This the first in a series of papers on special Lagrangian submanifolds in ℂm. We study special Lagrangian submanifolds in ℂm with large symmetry groups, and we give a number of explicit constructions. Our main results concern special Lagrangian cones in ℂm invariant under a subgroup G in SU(m) isomorphic to U(1)m−2. By writing the special Lagrangian equation as an ordinary differential equation (ODE) in G-orbits and solving the ODE, we find a large family of distinct, G-invariant special Lagrangian cones on Tm−2 in ℂm. These examples are interesting as local models for singularities of special Lagrangian submanifolds of Calabi-Yau manifolds. Such models are needed to understand mirror symmetry and the Strominger-Yau-Zaslow (SYZ) conjecture.
Publié le : 2002-10-01
Classification:  53C38,  53D12 
@article{1085598117,
     author = {Joyce, Dominic},
     title = {Special Lagrangian m-folds in $\mathbb{C}$<sup>
 m
</sup> with symmetries},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 1-51},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598117}
}

Joyce, Dominic. Special Lagrangian m-folds in ℂ
 m
 with symmetries. Duke Math. J., Tome 115 (2002) no. 1, pp.  1-51. http://gdmltest.u-ga.fr/item/1085598117/