共查询到20条相似文献,搜索用时 15 毫秒
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We classify the 2-dimensional Laguerre planes which can be obtained by gluing together halves of ovoidal Laguerre planes along two parallel classes.This research was supported by a Feodor Lynen fellowship and a DAAD fellowship. 相似文献
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Holger Bickel 《Results in Mathematics》1997,32(1-2):47-60
We present stiffness results for four-dimensional stable planes showing that a non-projective plane is suffer than a projective one. Whereas the best possible result in projective planes is that the isotropy group of a non-degenerate quadrangle has order at most two, we obtain that certain degenerate quadrangles with two non-compact sides have a zero-dimensional isotropy group. In [2] our stiffness results help to determine all four-dimensional stable planes with an at least nine-dimensional automorphism group. Our results improve those of Löwen [12], 5.2. We introduce the Freudenthal compactification as a new tool. 相似文献
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Andreas E. Schroth 《Geometriae Dedicata》1995,58(2):185-191
Every flat Laguerre plane of shear type over a pair of skew parabolae is related to a flat Laguerre plane of translation type over a pair of skew parabolae and vice versa. The relationship is defined using the connection between flat Laguerre planes and three-dimensional generalized quadrangles.Dedicated to Prof. H. R. Salzmann on his 65th birthday 相似文献
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Results in Mathematics - 相似文献
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Robert D. Knight 《Journal of Geometry》2005,83(1-2):137-152
A simple classification of triples of Lie cycles is given. The class of each triad determines the number of solutions to the
associated oriented Apollonius contact problem. The classification is derived via 2-dimensional Lie contact geometry in the
form of two of its subgeometries—Laguerre geometry and oriented M?bius geometry. The method of proof illustrates interactions
between the two subgeometries of Lie geometry. Two models of Laguerre geometry are used: the classic model and the 3-dimensional
affine Minkowski space model. 相似文献
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Robert D. Knight 《Journal of Geometry》2015,106(1):123-136
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A. E. Schroth 《Geometriae Dedicata》1990,36(2-3):365-373
Every three-dimensional generalized quadrangle can be constructed from flat Laguerre planes.Dedicated to Prof. H. Salzmann on his 60th birthday 相似文献
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R. Artzy 《Journal of Geometry》1974,5(2):109-116
A 4-point Pascal theorem on an oval in a protective plane led to the symmetry theorem in the Minkowski plane, and this relation was used by the author in [2,3] to prove that the symmetry theorem is equivalent to Miquel's theorem and that it implies the tangency theorem (Berührsatz). The same special Pascal theorem now leads to an incidence theorem, , for the Laguerre plane, which is again equivalent to Miquel's theorem. The configuration of contains 6 points and 5 circles and is thus simpler than that of Miquel, although it does not have the intuitive symmetry properties of the corresponding configuration in the Minkowski plane. 相似文献
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We show that each parabolic curve f in R2 produces a Laguerre plane
if f and all its images under dilatations are cycles. Likewise, two hyperbolic curves f1,f2 produce a Minkowski planeM(f1,f2). We determine for which curves
is miquelian resp. ovoidal, and for which pairs f1,f2,M(f1,f2) is miquelian resp. satisfies the rectangle axiom, thus providing many examples of non-embeddable planes. 相似文献
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Andreas E. Schroth 《Geometriae Dedicata》1993,46(3):339-361
The Lie geometry of a finite-dimensional locally compact connected Laguerre plane is a topological generalized quadrangle. 相似文献