논문KCI 등재
HOMOGENEOUS SUBMERSIONS OF 3-DIMENSIONAL GEOMETRIES
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초록
We study the geometry of the images of 1-dimensional homogeneous submersions for each of the model spaces X of the eight 3-dimensional geometries. In particular, We shall calculate the group of isometries and the curvatures of the base surfaces for each of the model spaces of 3-dimensional geometries, with respect to every closed subgroup of the isometries of X acting freely.
참고문헌 (5)
- D. Gromoll, "One-dimensional metric foliations in constant curvature spaces, Differential geometry and complex analysis", pp.165~168 (1985), Springer
- S. Helgason, "Differential Geometry, Lie groups, and Symmetric Spaces" (1978), Academic Press
- B. O'Neill, "The fundamental equations of a submersion", Michigan Math. J, 13, pp.445~457 (1966)
- J. Ratcliffe, "Foundations of Hyperbolic Manifolds" (2006), Springer
- P. Scott, "The geometries of 3-manifolds", Bull. London Math. Soc, 15(5), pp.401~487 (1983)
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