Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894747 | Journal of Geometry and Physics | 2015 | 4 Pages |
Abstract
We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with respect to one complex structure and which acts non-trivially on the corresponding symplectic form always has a fixed point locus which is complex Lagrangian with respect to one of the other complex structures, and (b) there exist Lagrangian submanifolds which are complex with respect to one complex structure and are not the fixed point locus of any involution which is anti-holomorphic with respect to one of the other complex structures.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Indranil Biswas, Graeme Wilkin,