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Collineation groups of topological parallelisms
-
Dieter Betten
and
Rolf Riesinger
Published/Copyright:
January 17, 2014
Abstract
Let P be a topological parallelism of the real projective 3-space PG3ℝ. We investigate the group AutP of all collineations of PG3ℝ leaving P invariant. We prove that AutP is a Lie group whose dimension is at most 6. The main result of the article says: if the dimension equals 6, then P is a Clifford parallelism. Furthermore, we show that there are no topological parallelisms in PG3ℝ with a 5-dimensional group.
Published Online: 2014-01-17
Published in Print: 2014-01
© 2014 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Real hypersurfaces of complex and quaternionic hyperbolic spaces
- Toric geometry of the 3-Kimura model for any tree
- Invariant surfaces in Sol3 with constant mean curvature and their computer graphics
- A short geometric proof that Hausdorff limits are definable in any o-minimal structure
- Seshadri constants on smooth threefolds
- Visible shoreline results for staircase paths in ℝd
- Characterization of isometric embeddings of Grassmann graphs
- Typical simplicially convex bodies
- On successive radii of p-sums of convex bodies
- Resolving sets for four families of distance-regular graphs
- White-black graphs and right-angled hyperbolic handlebodies
- Scalar and Ricci curvatures of special contact slant submanifolds in Sasakian space forms
- Non-factorial quartic double solids
- Collineation groups of topological parallelisms
