共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
Barbara Priwitzer 《Geometriae Dedicata》1995,58(3):245-258
LetP=(P, L) be a compact projective plane with 0P< and let be a compact connected subgroup of Aut(P). If dim dimE – dimP, whereE is the elliptic motion group of the corresponding classical plane, then E or is isomorphic to a point stabilizerE
0 inE, cf. [31]. Here we consider the case E
0. It is shown that the action of on the point spaceP is equivalent to the classical action ofE
0. For dimP {8, 16} the planeP is uniquely determined by a 2-dimensional subplane with SO2 Aut().Für H. Reiner Salzmann zum 65. Geburtstag 相似文献
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
Blowing up points and embedding flat stable planes in the nonorientable compact surface of genus one
We show that the point set of every flat stable plane embeds in the point set of the real projective plane. Connectedness of lines or of the point space is not assumed. We give two largely independent proofs; the first one is more conceptual, while the second one is more direct, and shorter. The first proof uses a new construction called blowing up a point, i.e., replacing it with its line pencil; this amounts to adding a cross cap. This construction seems to be of interest in its own right. 相似文献
13.
14.
Let M denote a connected (n+1)-manifold (without boundary). We study laminated decompositions of M, by which we mean upper semicontinous decompositions G of M into closed, connected n-manifolds. In particular, given M with a lamination G and N, a locally flat, closed, n-dimensional submanifold, we determine conditions under which M admits another lamination GN with N?GN. For n ≠ 3 a sufficient condition is that i: N → M be a homotopy equivalence. For n > 3 we give examples to show that i: N → M being a homology equivalence is not sufficient. We also show how to replace the assumption of local flatness of N with a weaker cellularity criterion (n ? 4) known as the inessential loops condition. We then give examples illustrating the abundance of pathology if M is not assumed to have a preexisting lamination. 相似文献
15.
Günter F. Steinke 《Geometriae Dedicata》1995,58(1):21-44
This paper concerns a generalization of Moulton planes constructed by J. Jakóbowski. We consider those planes over ordered fields and solve the isomorphism and collineation problem posed inGeom. Dedicata
42 (1992), 243–253.Dedicated to Prof. H. Salzmann on the occasion of his 65th birthday 相似文献
16.
S.A. Grigorian 《Topology and its Applications》2006,153(18):3598-3614
Finite-sheeted covering mappings onto compact connected groups are studied. We show that for a covering mapping from a connected Hausdorff topological space onto a compact (in general, non-abelian) group there exists a topological group structure on the covering space such that the mapping becomes a homomorphism of groups. To prove this fact we construct an inverse system of covering mappings onto Lie groups which approximates the given covering mapping. As an application, it is shown that a covering mapping onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by degree of the mapping. We also get a criterion for triviality of coverings in terms of means and prove that each finite covering of G is equivalent to a polynomial covering. 相似文献
17.
We prove the existence of uncountably many nonisomorphic topological projective planes, each universal in the sense that it contains an isomorphic copy of every pseudoline arrangement. 相似文献
18.
19.
We assume that in a linear space
there is a
non-empty set M of points with the property that every plane
containing a point of M is a projective plane. In
section 3 an example is given that in general
is not a
projective space. But if M can be completed by two
points to a generating set of P, then
is a projective space. 相似文献
20.
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