Hermitian structures on cotangent bundles of four dimensional solvable Lie groups

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dc.creatorde Andrés, L. C.
dc.creatorBarberis, M. L.
dc.creatorDotti, I.
dc.creatorFernández, M.
dc.date2006-04-27
dc.date2008-04-30
dc.date.accessioned2026-07-07T09:35:55Z
dc.date.available2026-07-07T09:35:55Z
dc.descriptionWe 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 Cavalcanti-Gualtieri and Fernández-Gotay-Gray, 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.
dc.description26 pages. Typos corrected
dc.identifierhttps://arxiv.org/abs/math/0604608
dc.identifierhttp://arxiv.org/abs/math/0604608
dc.identifierOsaka J. Math. 44, 765--793, 2007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159995
dc.subjectDifferential Geometry
dc.subject17B30; 53C15; 22E25; 53C55; 53D17
dc.titleHermitian structures on cotangent bundles of four dimensional solvable Lie groups
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