solvmanifolds — 1 articles found.

Classification of compact homogeneous manifolds with pseudo-Kählerian structures

C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (1) 2009, pp. 20–23
Vol.31 (1) 2009
Daniel Guan Details
(Received: 2008-11-11 )
(Received: 2008-11-11 )

Daniel Guan, Department of Mathematics, University of California at Riverside, Riverside, CA 92521, U.S.A.; e-mail: zguan@math.ucr.edu

Abstract/Résumé:

In this note we apply a modification theorem for compact homogeneous solvmanifolds to compact complex homogeneous manifolds with pseudo-Kählerian structures. We are then finally able to classify these compact pseudo-Kählerian manifolds as certain products of projective rational homogeneous spaces, tori, and simple and double reduced primitive pseudo-Kähler spaces.

Dans cette note, nous appliquons un théorème de modification pour des “solv-variétés” compactes et homogènes aux variétés compactes complexes equipées d’une structure pseudo-kählérienne. Nous obtenons une classification de ces variétés compactes pseudo-kählériennes sous la forme de certains produits d’espaces projectifs rationnels et homogènes, de tores, et d’espaces pseudo-kählériens réduits et primitifs simples ou doubles.

Keywords: Lie group, cohomology, compact manifolds, decompositions, fiber bundles, homogeneous space, invariant structure, modification, product, pseudo-Kahlerian, solvmanifolds, splittings, symplectic manifolds, uniform discrete subgroups

AMS Subject Classification: General geometric structures on manifolds (almost complex; almost product structures; etc.) 53C15

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