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

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

2004-01-22

arxiv.org/abs/math/0401294v1

Commun. Math. Phys. 262, 1-16 (2006)

Mathematics

Differential Geometry

Scientific paper

10.1007/s00220-005-1472-9

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.

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