Maximal holonomy of infra-nilmanifolds with $2$-dimensional quaternionic Heisenberg geometry
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- by Ku Yong Ha, Jong Bum Lee and Kyung Bai Lee PDF
- Trans. Amer. Math. Soc. 357 (2005), 355-383 Request permission
Abstract:
Let $\mathbf {H}_{4n-1}(\mathbb {H})$ be the quaternionic Heisenberg group of real dimension $4n-1$ 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 $I_2=48$. As an application, by applying Kim and Parker’s result, we obtain that the minimum volume of a $2$-dimensional quaternionic hyperbolic manifold with $k$ cusps is at least $\frac {\sqrt {2}k}{720}.$References
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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
- MR Author ID: 343537
- Email: jlee@sogang.ac.kr
- Kyung Bai Lee
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- Email: kb_lee@math.ou.edu
- 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. - © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 355-383
- MSC (2000): Primary 20H15, 20F18, 20E99, 53C55
- DOI: https://doi.org/10.1090/S0002-9947-04-03511-1
- MathSciNet review: 2098099