共查询到20条相似文献,搜索用时 15 毫秒
1.
Hauke Klein 《Geometriae Dedicata》1995,58(1):53-62
We consider 4-dimensional compact projective planes with a solvable 6-dimensional collineation group and with orbit type (2, 1), i.e. fixes a flagv W, acts transitively onL
\{W} and fixes no point in the setW\{v}. We We prove a series of lemmas concerning the action of invariant subgroups of . These lemmas are applied to prove that the maximal connected nilpotent invariant subgroup of has dimension at least 4.Dedicated to Prof. H. Salzmann on the occasion of his 65th birthday 相似文献
2.
Markus Stroppel 《Geometriae Dedicata》1995,58(2):117-125
We show that the existence of an almost simple group of automorphisms of dimension greater than 10 characterizes the Hughes planes (including the quarternion plane) among the 8-dimensional compact projective planes.Dedicated to Prof. Helmut R. Salzmann on his 65th birthday 相似文献
3.
Barbara Priwitzer 《Geometriae Dedicata》1994,52(1):33-40
We prove the following theorem: LetP be an 8-dimensional compact topological projective plane. If the connected component of its automorphism group has dimension at least 12, then is a Lie group. 相似文献
4.
D. Betten 《Geometriae Dedicata》1995,58(3):259-289
The article is a contribution to the classification of all 4-dimensional flexible compact projective planes. We assume that the collineation group is a 6-dimensional solvable Lie group which fixes some flag. If, moreover, the nilradical of the collineation group is 5-dimensional, then we get 4 families of new planes which are neither translation planes nor shift planes.Meinem Lehrer H. Salzmann zum 65. Geburtstag am 3.11.1995 in Dankbarkeit gewidmet 相似文献
5.
Hauke Klein 《Geometriae Dedicata》1996,61(3):227-255
We consider a four-dimensional compact projective plane =(
,
) whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil × R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag pW, acts transitively on
p
\{W}, and fixes no point in the set W{p}. We study the actions of and N on
and on the pencil
p
\{W}, in the case that does not contain a three-dimensional elation group. In the special situation that acts doubly transitively on
p
{W}, we will determine all possible planes . There are exactly two series of such planes. 相似文献
6.
Hermann Hähl 《Topology and its Applications》1981,12(1):49-63
In a compact, connected topological projective plane, let Ω be a closed Lie subgroup of the group of all axial collineations with a fixed axis A. We compare the set З\A consisting of the centres of all non-identical homologies in Ω to orbits of the group of all elations contained in Ω and of its connected component . It is shown that З\A is the union of at most countably many θ-orbits; moreover, З\A turns out to be a single θ-orbit whenever the connected component of Ω contains non-identical homologies. This result is analogous to a well-known theorem of André for finite planes. It has numerous consequences for the structure of collineation groups of compact, connected projective planes. 相似文献
7.
We determine centralizers and unitals for the polarities of eight-dimensional compact
planes with at least 17-dimensional group of automorphisms, and discuss transitivity properties.Received: 7 August 2003 相似文献
8.
We determine all planes having the properties of the title with a group of dimension at least 33.Received: 25 September 2003 相似文献
9.
Franz B. Kalhoff 《Geometriae Dedicata》1995,54(2):199-224
The valuation topology of any uniformly valued ternary field (K, T, v) can be extended to the projective plane II over (K, T) making it a topological projective plane in the sense of Salzmann. Appealing to Prieß-Crampe's celebrated fixed point theorem for ultrametric spaces, our result allows us to present a wide variety of new, totally disconnected, compact and non-compact topological projective planes.Dedicated to Professor S. Prieß-Crampe on the occasion of her 60th birthday 相似文献
10.
Burkard Polster 《Geometriae Dedicata》1995,56(2):155-175
In this paper we describe several elementary constructions of 4-, 8- and 16-dimensional locally compact affine planes. The new planes share many properties with the classical ones and are very easy to handle. Among the new planes we find translation planes, planes that are constructed by gluing together two halves of different translation planes, 4-dimensional shift planes, etc. We discuss various applications of our constructions, e.g. the construction of 8- and 16-dimensional affine planes with a point-transitive collineation group which are neither translation planes nor dual translation planes, the proof that a 2-dimensional affine plane that can be coordinatized by a linear ternary field with continuous ternary operation can be embedded in 4-, 8- and 16-dimensional planes, the construction of 4-dimensional non-classical planes that admit at the same time orthogonal and non-orthogonal polarities. We also consider which of our planes have tangent translation planes in all their points. In a final section we generalize the Knarr-Weigand criterion for topological ternary fields.This research was supported by a Feodor Lynen fellowship. 相似文献
11.
Joachim Otte 《Geometriae Dedicata》1995,58(2):203-212
A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over , , or
.Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday 相似文献
12.
We prove that a compact, connected submanifold of the point space of a
smooth projective plane is homeomorphic to a sphere provided that
certain intersection properties with lines are satisfied. As an
application, we show that the set of absolute points of a smooth
polarity in a smooth projective plane of dimension 2l is empty or
homeomorphic to a sphere of dimension 2l - 1 or
.Received: 13 September 2002 相似文献
13.
Harald Löwe 《Geometriae Dedicata》1994,52(1):87-104
A shear plane is a 2n-dimensional stable plane admitting a quasi-perspective collineation group which is a vector group of the same dimension 2n and fixes no point. We show that all of these planes can be derived from a special kind of partial spreads by a construction analogous to the construction of (punctured) dual translation planes from compact spreads. Finally we give a criterion (and examples) for shear planes which are not isomorphic to an open subplane of a topological projective plane. 相似文献
14.
Theo Grundhofer 《Geometriae Dedicata》1986,21(3):291-298
Compact connected projective planes have been investigated extensively in the last 30 years, mostly by studying their automorphism groups. It is our aim here to remove the connectedness assumption in some general results of Salzmann [31] and Hähl [14] on automorphism groups of compact projective planes. We show that the continuous collineations of every compact projective plane form a locally compact transformation group (Theorem 1), and that the continuous collineations fixing a quadrangle in a compact translation plane form a compact group (Corollary to Theorem 3). Furthermore we construct a metric for the topology of a quasifield belonging to a compact projective translation plane, using the modular function of its additive group (Theorem 2). 相似文献
15.
16.
Harald Löwe 《Geometriae Dedicata》1995,58(1):45-51
We construct symmetric planes associated with an arbitrary locally compact connected nearfield
. If
is a proper nearfield, i.e.
{;;}, then the tangent translation plane of this symmetric plane is not classical. All previously known examples of symmetric planes have classical tangent translation planes.Herrn Professor Dr. H. Salzmann zum 65. Geburtstag gewidmet 相似文献
17.
The flag-homogeneous compact connected polygons with equal topological parametersp = q are classified explicitly. These polygons turn out to be Moufang polygons. 相似文献
18.
19.
The translation planes with spreads in PG(3, q) that admit at least two Baer groups of order q–1 are classified. 相似文献