MAXIMAL HOLONOMY OF INFRA-NILMANIFOLDS WITH so(3)×ℝ3-GEOMETRY

Title & Authors
MAXIMAL HOLONOMY OF INFRA-NILMANIFOLDS WITH so(3)×ℝ3-GEOMETRY
Lee, Kyung-Bai; Shin, Joon-Kook;

Abstract
Let $\small{so(3)\tilde{\times}R^3}$ be the 6-dimensional nilpotent Lie group with group operation (s, x)(t, y) = $\small{(s+t+xy^t-yx^t,\;x+y)}$. We prove that the maximal order of the holonomy groups of all infra-nilmanifolds with $\small{so(3)\tilde{\times}R^3}$-geometry is 16.
Keywords
almost Bieberbach group;holonomy group;infra-nilmanifold;
Language
English
Cited by
1.
Maximal holonomy of infra-nilmanifolds with 3-dimensional Iwasawa geometry, Forum Mathematicum, 2011, 23, 3
References
1.
H. Brown, R. Bulow, J. Neubuser, H. Wondratschek, and H. Zassenhaus, Crys- tallographic Groups of Four-Dimensional Spaces, John Wiley & Sons, Inc., New York, 1978

2.
K. Y. Ha, J. B. Lee, and K. B. Lee, Maximal holonomy of infra-nilmanifolds with 2-dimensional Quaternionic Heisenberg Geometry, Trans. Amer. Math. Soc. 357 (2005), no. 1, 355-383

3.
I. Kim and J. R. Parker, Geometry of quaternionic hyperbolic manifolds, Math. Proc. Cambridge Philos. Soc. 135 (2003), no. 2, 291-320

4.
K. B. Lee and F. Raymond, Topological, affine and isometric actions on flat Riemannian manifolds, J. Differential Geom. 16 (1981), no. 2, 255-269

5.
K. B. Lee, J. K. Shin, and S. Yokura, Free actions of finite abelian groups on the 3-torus, Topology Appl. 53 (1993), no. 2, 153-175

6.
K. B. Lee and A. Szczepanski, Maximal holonomy of almost Bieberbach groups for $Heis_5$, Geom. Dedicata 87 (2001), no. 1-3, 167-180

7.
S. Wolfram, Mathematica, Wolfram Research, 1993