대한수학회지 (Journal of the Korean Mathematical Society)

  • 제36권1호
  • /
  • Pages.1-13
  • /
  • 1999
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

3-DIMENSIONAL NON-COMPACT INFRA-NILMANIFOLDS

  • 발행 : 1999.01.01
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초록

Let G be the 3-dimensional Heisenberg group. A discrete subgroup of Isom(G), acting freely on G with non-compact quotient, must be isomorphic to either 1, Z, Z2 or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into Isom(G) up to affine conjugacy. This yields an affine calssification of 3-dimensional non-compact infra-nilmanifolds.

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참고문헌

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  2. Annals of Math. v.83 Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups Ⅱ L. Auslander
  3. Bieberbach Groups and Flat Manifolds Leonard S. Charlap
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  5. Quarterly J. Math. (Oxford)(2) v.46 Infra-solvmanifolds of type (R) K. B. Lee
  6. Bull. London Math. Soc. v.15 The geometries of 3-manifolds P. Scott
  7. Spaces of constant curvature J. Wolf