Open Access
Translator Disclaimer
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).

Abstract

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.

Citation

Download Citation

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.

Information

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

zbMATH: 1151.53064
MathSciNet: MR2383809

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

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

JOURNAL ARTICLE
29 PAGES


SHARE
Vol.44 • No. 4 • December 2007
Back to Top