Anti-holomorphic involutive isometry of hyper-Kähler manifolds and branes

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JournalJournal of Geometry and Physics
DatePublished - 2 Nov 2014
Volume88
Number of pages4
Pages (from-to)52-55
Original languageEnglish

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.

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