Double products and hypersymplectic structures on $R^{4n}$

Abstract

In this paper we give a procedure to construct hypersymplectic structures on $R^{4n}$ beginning with affine-symplectic data on $R^{2n}$. These structures are shown to be invariant by a 3-step nilpotent double Lie group and the resulting metrics are complete and not necessarily flat. Explicit examples of this construction are exhibited.

References in corpus (4)

• Kleinian Geometry and the N=2 Superstring
• Actions For (2,1) Sigma-Models and Strings
• Abelian complex structures on solvable Lie algebras
• Complex Product Structures on Lie Algebras

Cited by in corpus (14)

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• On paraquaternionic submersions between paraquaternionic Kähler manifolds
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• Weak Mirror Symmetry of Complex Symplectic Algebras
• The geometry of recursion operators
• Special symplectic Lie groups and hypersymplectic Lie groups
• Metric geometries over the split quaternions
• Symmetric and skew-symmetric complex structures
• k-symplectic structures and absolutely trianalytic subvarieties in hyperkahler manifolds
• Pseudo-Kähler and hypersymplectic structures on semidirect products
• Connections functorially attached to almost complex product structures
• Product structures on four dimensional solvable Lie algebras
• Abelian Hermitian geometry