Kähler flat manifolds

DOI10.2969/jmsj/06120363zbMath1187.53051OpenAlexW2018221395MaRDI QIDQ1030012

Karel Dekimpe, Andrzej Szczepański, Marek Hałenda

Publication date: 1 July 2009

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: http://www.jstage.jst.go.jp/article/jmath/61/2/61_363/_article

zbMATH Keywords

Kähler manifoldBieberbach groupflat manifoldHantzsche--Wendt manifoldHodge diamondhyperelliptic variety

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Kähler manifolds (32Q15) Issues of holonomy in differential geometry (53C29) Other geometric groups, including crystallographic groups (20H15) Geometric structures on manifolds of high or arbitrary dimension (57N16) Classification theorems for complex manifolds (32Q57)

Related Items (14)

Crystallographic groups and flat manifolds from surface braid groups ⋮ Flat equivariant gerbes: holonomies and dualities ⋮ Flat F-theory and friends ⋮ Covariant star product on semi-conformally flat noncommutative Calabi–Yau manifolds and noncommutative topological index theorem ⋮ Holonomy groups of compact flat solvmanifolds ⋮ Classification of 6-dimensional splittable flat solvmanifolds ⋮ Lagrangian foliations and Anosov symplectomorphisms on Kähler manifolds ⋮ Complex Hantzsche-Wendt manifolds ⋮ Chern-flat and Ricci-flat invariant almost Hermitian structures ⋮ A flat projective variety with \(D_8\)-holonomy ⋮ The classification of hyperelliptic threefolds ⋮ On Bieberbach subgroups of \(B _n/[P _n,P _n\) and flat manifolds with cyclic holonomy \(\mathbb{Z}_{2^d}\)] ⋮ Bieberbach groups and flat manifolds with finite abelian holonomy from Artin braid groups ⋮ \(G_2\)-structures on flat solvmanifolds

Uses Software

• CARAT

Cites Work

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• Computation of Five-and Six-Dimensional Bieberbach Groups
• HOLONOMY OF FLAT MANIFOLDS WITH b₁ = 0
• Kähler groups and rigidity phenomena
• The spectrum of twisted Dirac operators on compact flat manifolds
• Spin structures on flat manifolds

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