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December 2007 Hermitian structures on cotangent bundles of four dimensional solvable Lie groups
Luis C. de Andrés, M. Laura Barberis, Isabel Dotti, Marisa Fernández
Osaka J. Math. 44(4): 765-793 (December 2007).


We study hermitian structures, with respect to the standard neutral metric on the cotangent bundle $T^*G$ of a 2n-dimensional Lie group $G$, which are left invariant with respect to the Lie group structure on $T^*G$ induced by the coadjoint action. These are in one-to-one correspondence with left invariant generalized complex structures on $G$. Using this correspondence and results of [8] and [10], it turns out that when $G$ is nilpotent and four or six dimensional, the cotangent bundle $T^*G$ always has a hermitian structure. However, we prove that if $G$ is a four dimensional solvable Lie group admitting neither complex nor symplectic structures, then $T^*G$ has no hermitian structure or, equivalently, $G$ has no left invariant generalized complex structure.


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Luis C. de Andrés. M. Laura Barberis. Isabel Dotti. Marisa Fernández. "Hermitian structures on cotangent bundles of four dimensional solvable Lie groups." Osaka J. Math. 44 (4) 765 - 793, December 2007.


Published: December 2007
First available in Project Euclid: 7 January 2008

zbMATH: 1151.53064
MathSciNet: MR2383809

Primary: 17B30 , 22E25 , 53C15
Secondary: 53C55 , 53D17

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics


Vol.44 • No. 4 • December 2007
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