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A CYCLIC GROUP ACTION ON THE NILMANIFOLD
JOONKOOK SHIN,JONG IL KIM 충청수학회 2000 충청수학회지 Vol.13 No.2
we study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant
FREE ACTIONS OF FINITE GROUPS ON THE 3–DIMENSIONAL NILMANIFOLD FOR TYPE 1
Joonkook Shin 충청수학회 2006 충청수학회지 Vol.19 No.4
We study free actions of finite groups on the 3-dimensional nilmanifold for Type 1 and classify all such group actions, up to topological conjugacy. This work supplies missing one in [1, Theorem 3.11.].
Joonkook Shin,Sungsook Hong 충청수학회 2003 충청수학회지 Vol.16 No.1
We shall study the automorphism group of the quaternionic Heisenberg group H 7 (H) = R 3 ˜×H which is important to investigate an almost Bieberbach group of a 7-dimensinal infra-nilmanifold and show that Aut(R 3 ˜×R 4 ) ∼= Hom(R 4 , R 3 ) ⋊ O(J; 2, 2).
FREE CYCLIC ACTIONS OF THE 3-DIMENSIONAL NILMANIFOLD
JOONKOOK SHIN,DAEHWAN GOO,EUNMI PARK 충청수학회 2001 충청수학회지 Vol.14 No.2
we shall deal with ten cases out of 15 distinct almost Bieberbach groups up to 8eifert local invariant. In those cases we will show that if G is a finite abelian group acting freely on the standard nilmanifold, then G is cyc1ic, up to topological conjugacy.
ISOMETRY GROUPS OF UNIMODULAR SIMPLY CONNECTED 3-DIMENSIONAL LIE GROUPS
SHIN, JOONKOOK 충남대학교 기초과학연구소 1995 연구논문집 Vol.15 No.-
We characterize the left invariant Riemannian metrics on each of the six unimodular simply connected 3-dimensional Lie groups which give rise to 3-, 4-, or 6-dimensional isometry groups. It turns out that this classification is independent of curvature properties.
A CYCLIC GROUP ACTION ON THE NILMANIFOLD
Shin, Joonkook,Kim, Jong-Il 충청수학회 2001 충청수학회지 Vol.13 No.2
We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.
Shin, Joonkook,Hong, Sungsook 충청수학회 2003 충청수학회지 Vol.16 No.1
We shall study the automorphism group of the quaternionic Heisenberg group $\mathcal{H}_7(\mathbb{H})=\mathbb{R}^3{\tilde{\times}}\mathbb{H}$ which is important to investigate an almost Bieberbach group of a 7-dimensinal infra-nilmanifold and show that Aut$$(\mathbb{R}^3{\tilde{\times}}\mathbb{R}^4){\sim_=}Hom(\mathbb{R}^4,\mathbb{R}^3){\rtimes}O(J;2,2)$$.
FREE ACTIONS OF FINITE GROUPS ON THE 3-DIMENSIONAL NILMANIFOLD FOR TYPE 1
Shin, Joonkook 충청수학회 2006 충청수학회지 Vol.19 No.4
We study free actions of finite groups on the 3-dimensional nilmanifold for Type 1 and classify all such group actions, up to topological conjugacy. This work supplies missing one in [1, Theorem 3.11.].
FREE ACTIONS ON THE NILMANIFOLD
Shin, Joonkook 충청수학회 1997 충청수학회지 Vol.10 No.1
We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.