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

Authors:
Ku Yong Ha, Jong Bum Lee and Kyung Bai Lee

Journal:
Trans. Amer. Math. Soc. **357** (2005), 355-383

MSC (2000):
Primary 20H15, 20F18, 20E99, 53C55

Published electronically:
May 10, 2004

MathSciNet review:
2098099

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Abstract: Let be the quaternionic Heisenberg group of real dimension and let denote the maximal order of the holonomy groups of all infra-nilmanifolds with -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

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Additional Information

**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:
http://dx.doi.org/10.1090/S0002-9947-04-03511-1

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

Published electronically:
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.

Article copyright:
© Copyright 2004
American Mathematical Society