Maximal holonomy of infra-nilmanifolds with $2$-dimensional quaternionic Heisenberg geometry

DOI10.1090/S0002-9947-04-03511-1zbMath1078.20053OpenAlexW1500675964MaRDI QIDQ4819758

Kyung Bai Lee, Jong Bum Lee, Ku Yong Ha

Publication date: 5 October 2004

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03511-1

zbMATH Keywords

fundamental groupsholonomy groupscrystallographic groupshyperbolic manifoldsalmost Bieberbach groupsvolume estimatesquaternionic Heisenberg groupminimal volumes

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Nilpotent groups (20F18) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Discrete subgroups of Lie groups (22E40) Issues of holonomy in differential geometry (53C29) Other geometric groups, including crystallographic groups (20H15) Discontinuous groups of transformations (57S30) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (1)

Maximal holonomy of infra-nilmanifolds with 3-dimensional Iwasawa geometry

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Topological, affine and isometric actions on flat Riemannian manifolds
• Free actions of finite Abelian groups on the 3-torus
• Classification of free actions of finite groups on the 3-torus
• On the volumes of complex hyperbolic manifolds
• A Tangential Convergence for Bounded Harmonic Functions on a Rank one Symmetric Space
• Geometry of quaternionic hyperbolic manifolds
• Maximal holonomy of almost Bieberbach groups for \(\text{Heis}_5\)

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