Transactions of the American Mathematical Society

Maximal holonomy of infra-nilmanifolds with

-dimensional quaternionic Heisenberg geometry

Author(s): Ku Yong Ha; Jong Bum Lee; Kyung Bai Lee
Journal: Trans. Amer. Math. Soc. 357 (2005), 355-383.
MSC (2000): Primary 20H15, 20F18, 20E99, 53C55
Posted: May 10, 2004
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Abstract: Let $\mathbf{H}_{4n-1}(\mathbb{H} )$ be the quaternionic Heisenberg group of real dimension

and let $I_{n}$ denote the maximal order of the holonomy groups of all infra-nilmanifolds with $\mathbf{H}_{4n-1}(\mathbb{H} )$ -geometry. We prove that

. As an application, by applying Kim and Parker's result, we obtain that the minimum volume of a

-dimensional quaternionic hyperbolic manifold with

cusps is at least $\frac{\sqrt{2}k}{720}.$

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20H15, 20F18, 20E99, 53C55

Ku Yong Ha
Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Email: kyha@sogang.ac.kr

Jong Bum Lee
Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Korea
Email: jlee@sogang.ac.kr

Kyung Bai Lee
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: kb_lee@math.ou.edu

DOI: 10.1090/S0002-9947-04-03511-1
PII: S 0002-9947(04)03511-1
Keywords: Almost Bieberbach group, holonomy group, quaternionic Heisenberg group, quaternionic hyperbolic manifold
Received by editor(s): March 23, 2003
Received by editor(s) in revised form: August 25, 2003
Posted: May 10, 2004
Additional Notes: This research was supported in part by grant No. R01-1999-000-00002-0(2002) from the interdisciplinary Research program, and by grant No. R14-2002-044-01002-0(2002) from ABRL of KOSEF
This work was done while the second-named author was visiting the Department of Mathematics at the University of Oklahoma. He expresses his sincere thanks for their hospitality.
Copyright of article: Copyright 2004, American Mathematical Society

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