Geometric structures on low-dimensional manifolds

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Geometric structures on 3-manifolds are often projectively flat structures. Projectively flat structures on 3-manifolds are given by atlases of charts to RP3 with projective transition maps. Equivalently, they are given by projectively flat torsion-free connections. We study the question of putting projective structures on 3-manifolds. This is done by triangulating a given 3 manifold, and then reducing the question to a 2-dimensional classical projective geometry problem produced by the Haken diagram of the 3-manifold. Next, we show that the 2-dimensional problem can be reduced to solving a system of homogeneous equations that are in product forms of scalar triple products of vectors. Finally, we will compute the deformation spaces of projective structures on a small class of 3-orbifolds.
Publisher
KOREAN MATHEMATICAL SOC
Issue Date
2003-03
Language
English
Article Type
Article
Citation

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.40, no.2, pp.319 - 340

ISSN
0304-9914
URI
http://hdl.handle.net/10203/7663
Appears in Collection
MA-Journal Papers(저널논문)
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