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A note about invariant SKT structures and generalized Kähler structures on flag manifolds

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  21 March 2012

Dmitri V. Alekseevsky  and
Liana David
Dmitri V. Alekseevsky
Affiliation:
School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK (d.aleksee@ed.ac.uk)
Liana David
Affiliation:
Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, Calea Grivitei nr. 21, 010702 Bucharest, Romania (liana.david@imar.ro)
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Abstract

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We prove that any invariant strong Kähler structure with torsion (SKT structure) on a flag manifold M = G/K of a semi-simple compact Lie group G is Kähler. As an application we describe invariant generalized Kähler structures on M.

Keywords

SKT structures(generalized) Kahler structuresflag manifold

MSC classification

Secondary: 53D18: Generalized geometries (à la Hitchin)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 3 , October 2012 , pp. 543 - 549
Copyright
Copyright © Edinburgh Mathematical Society 2012

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