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1.
Hermann Hähl 《Geometriae Dedicata》1987,23(3):319-345
We study 16-dimensional locally compact translation planes in which, for an affine point o, the stabilizer
of the affine collineation group
contains a subgroup locally isomorphic to SU4 (). If has only one affine fixed point o, then it is shown that either the plane is the classical Moufang plane over the Cayley numbers, or else must be normal in the stabilizer
and
has dimension at most 37. This also comprises the proof of the fact that if
contains a subgroup locally isomorphic to SU4() × SL2() then the plane is the classical Cayley plane. The case that has more affine fixed points in dealt with as well; then, except for a well-known family of planes admitting Spin7() as a group of collineations,
has dimension at most 34. 相似文献
2.
Renate Jaritz 《Geometriae Dedicata》1997,64(3):365-372
An ordered plane is an incidence structure (
) with an order function , which satisfies the axioms (G), (V) and (S), but no continuation--axiom is required. Points a, b E are said to be in distinct sides of a line
iff
and in the same side if
, respectively. For any lines
,
and
we prove that if b,c are in the same side of line A and a,c are in the same side of B , then a and b are in distinct sides of C. As conclusions we deduce that is harmonic and that in each complete quadrangle the intersection points of the diagonals are never collinear, which is known as the axiom of Fano. So the Fano-axiom holds in each ordered plane, and also in those with boundary points. 相似文献
3.
Hermann Hähl 《Geometriae Dedicata》1995,58(2):213-226
As a contribution to a classification of all sixteen-dimensional translation planes whose collineation group
has dimension at least 38, this paper deals with the case that
contains a subgroup (locally) isomorphic to SU2Spin5. Under various further assumptions, it is shown that such a plane satisfying dim
38 is necessarily isomorphic to the classical plane over the octonions.The complete classification will reveal that these further assumptions may in fact be omitted, except for the case that
even contains a subgroup isomorphic to Spin7. The latter planes have been explicitly determined in previous papers.
Meinem verehrten Lehrer Helmut Salzmann zum 65. Geburtstag 相似文献
4.
Rudolf Scharlau 《Geometriae Dedicata》1987,24(1):77-84
Following earlier work of Tits [8], this paper deals with the structure of buildings which are not necessarily thick; that is, possessing panels (faces of codimension 1) which are contained in two chambers, only. To every building , there is canonically associated a thick building
whose Weyl group W(
) can be considered as a reflection subgroup of the Weyl group W() of . One can reconstruct from
together with the embedding W(
) W(). Conversely, if
is any thick building and W any reflection group containing W(
) as a reflection subgroup, there exists a weak building with Weyl group W and associated thick building
. 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.
Maria Moszyńska 《Geometriae Dedicata》2000,83(1-3):131-147
Let
be a family of star bodies in R
n
(compact bodies in R
n
with nonempty kernels). A function s:
R
n
is a selector for
provided that s(A) ker A for every A
. To every star body A and every : [0,) [0,) we assign a function A: ker A R defined in terms of the radial function of translates of A. We prove that if A is convex and is concave and strictly increasing, then
A
has a unique maximizer, which is referred to as the radial center of A induced by (Theorem 3.1). We extend the radial center map over some family of star bodies (Theorem 4.2). Further, we define a suitable metric,
st
, the star metric, on the family of all the compact star sets in R
n
. This new metric is topologically stronger than the Hausdorff metric (Theorem 5.7). We study the continuity of our selectors with respect to
st
. 相似文献
7.
Suppose G is a connected, simple, real Lie group with
-rank(G) 2, M is an ergodic G-space with invariant probability measure , and : G × M Homeo(
) is a Borel cocycle. We use an argument of É. Ghys to show that there is a G-invariant probability measure on the skew product M ×
, such that the projection of to M is . Furthermore, if (G × M) Diff1(
), then can be taken to be equivalent to × , where is Lebesgue measure on
; therefore, is cohomologous to a cocycle with values in the isometry group of
. 相似文献
8.
Let < SL
n
(
) be a subgroup of finite index, where n 5. Suppose acts continuously on a manifold M, where 1(M) =
n
, preserving a measure that is positive on open sets. Further assume that the induced action on H
1(M) is non-trivial. We show there exists a finite index subgroup < and a equivariant continuous map : M
n
that induces an isomorphism on fundamental group. We prove more general results providing continuous quotients in cases where 1(M) surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with actions. 相似文献
9.
Alain Rivière 《Geometriae Dedicata》2001,85(1-3):217-235
For a separable Hilbert space E whose dimension is 2 and for an open subset of E, not empty and different from E, let
be the set of all points of which have at least two projections on the close set E\, and let
be the set of all the centres of the open balls contained in and which are maximal for inclusion. We show that the Hausdorff dimension dimH(
) of
may be any real value s such that 0sdim E; we also show that can be chosen so that
is everywhere dense in and so that we have dimH(
)=1.Associons à un ouvert d'un espace de Hilbert séparable E de dimension 2, non vide et distinct de E, l'ensemble
des points de admettant plusieurs projections sur le fermé E\, et l'ensemble
des centres des boules ouvertes inclues dans et maximales pour l'inclusion. Nous montrons d'une part que la dimension de Hausdorff dimH(
) de
peut prendre toute valeur réelle s telle que 0sdim E, et d'autre part qu'on peut choisir de sorte que
soit dense dans et qu'on ait dimH(
)=1. 相似文献
10.
This paper deals with polarized pairs
, where
is a nonsingular projective threefold and
is a very ample line bundle on it, such that for one smooth member  |
|, one has (Â)=2. A large class of pairs whose adjoint line bundle is nef and big was indirectedly studied by Beltrametti and co-workers. We add some more information, both in this general case and also when the adjoint line bundle fails to be nef and big. 相似文献
11.
Raúl Figueroa 《Geometriae Dedicata》1994,50(2):205-216
Let be a non-Desarguesian semifield plane of orderp
n, p a prime number 5 andn3, and let
denote the group induced by the autotopism groupG of on the line at infinity. We prove that is a generalized twisted field plane if, and only if,
has an element of order (p
k–1)((p
n–1)/(p
m–1)), for some integersk andm, wherek | m, m | n, andm.This work was supported in part by NSF grants RII-9014056, component IV of the EPSCoR of Puerto Rico grant and ARO grant for Cornell MSI 相似文献
12.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
13.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
14.
Martin Funk 《Geometriae Dedicata》1988,28(1):53-75
A projective confined configuration with axis and centre will be introduced in terms of a non-degenerate octagon
satisfying some hypotheses on the position of its diagonal points (i.e. intersections of edges having distance 8 in the flag graph (
)) and its first minor diagonal lines (i.e. diagonal lines joining vertices of distance 6 in (
)). That confined configuration gives rise to a certain configurational condition whose affine specialization (i.e. the axis coincides with the line at infinity) is equivalent to the affine Pappos condition, whereas its little specialization (i.e. the centre lies on the axis) turns out to be equivalent to the little Desargues condition. In Pappian projective planes can be completed to a configuration of type (124, 163). 相似文献
15.
Simon Thomas 《Geometriae Dedicata》1996,63(3):247-253
Let
be a finite field, and let (, B) be a nontrivial 2-(n, k, 1)-design over
. Then each point induces a (k–1)-spread S on /. (, B) is said to be a geometric design if S is a geometric spread on / for each . In this paper, we prove that there are no geometric designs over any finite field
.Research partially supported by NSF grant DMS-8703229. 相似文献
16.
R. Riesinger 《Geometriae Dedicata》1991,40(2):145-163
A spread
of a projective 3-space is said to be rigid (German: starr) if the only collineation of leaving
invariant is the identity; it is called nearly rigid if there are only finitely many collineations of this kind. A spread
of real projective 3-space is called topological if the associated translation plane in the sense of André (or Bruck and Bose) is a topological plane; it is then a 4-dimensional translation plane (abbreviated: 4-dtp) in the terminology of Betten.
is rigid if and only if every collineation of the associated 4-dtp fixes the translation line pointwise. In 1977 D. Betten asked for such 4-dtps and termed them rigid. If
is nearly rigid, the collineation group of the associated 4-dtp is 5-dimensional.In the present paper, examples of rigid and nearly rigid 4-dtps are constructed. The central tool is the method of crosswise tacking together two topological spreads of along a common regulus, which yields two further topological spreads. In a first step, this method when applied to known spreads produces nearly rigid spreads. Rigid spreads are then obtained by iteration of the method; the simplest example is composed of parts of four elliptic linear line congruences. The rigidness of a spread
of is proved by arguments from projective differential geometry applied to the image (
) under Klein's correspondence from line geometry. 相似文献
17.
Danny Calegari 《Geometriae Dedicata》2003,96(1):1-53
We generalize the main results from the author's paper in Geom. Topol. 4 (2000), 457–515 and from Thurston's eprint math.GT/9712268 to taut foliations with one-sided branching. First constructed by Meigniez, these foliations occupy an intermediate position between -covered foliations and arbitrary taut foliations of 3-manifolds. We show that for a taut foliation
with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations ± of M transverse to
with solid torus complementary regions which bind every leaf of
in a geodesic lamination. These laminations come from a universal circle, a refinement of the universal circles proposed by Thurston (unpublished), which maps monotonely and 1(M)-equivariantly to each of the circles at infinity of the leaves of
, and is minimal with respect to this property. This circle is intimately bound up with the extrinsic geometry of the leaves of
. In particular, let
denote the pulled-back foliation of the universal cover, and co-orient
so that the leaf space branches in the negative direction. Then for any pair of leaves of
with , the leaf is asymptotic to in a dense set of directions at infinity. This is a macroscopic version of an infinitesimal result from Thurston and gives much more drastic control over the topology and geometry of
, than is achieved by him. The pair of laminations ± can be used to produce a pseudo-Anosov flow transverse to
which is regulating in the nonbranching direction. Rigidity results for ± in the -covered case are extended to the case of one-sided branching. In particular, an -covered foliation can only be deformed to a foliation with one-sided branching along one of the two laminations canonically associated to the -coveredfoliation constructed in Geom. Topol. 4 (2000), 457–515, and these laminations become exactly the laminations ± for the new branched foliation. Other corollaries include that the ambient manifold is -hyperbolic in the sense of Gromov, and that a self-homeomorphism of this manifold homotopic to the identity is isotopic to the identity. 相似文献
18.
The generating line of the first single shift plane (cf. [11, p. 435]) is a 2-surface of
4 which we call the the affine part
of Knarr's surface. We compute all affinities leaving
invariant. After embedding
4 into PG(4,
) we calculate the uniquely determined projective closure
Kn
of
. Using a suitable projection we transform questions on Knarr's surface to questions on Cayley's surface in PG(3,
). In this way we determine all planes carrying 1-dimensional algebraic varieties of
Kn
. We exhibit all automorphic collineations of
Kn
. 相似文献
19.
E. G. Emel'yanov 《Journal of Mathematical Sciences》1987,38(4):2081-2090
Let A={a1,...,an} and B={b1,...,bm} be systems of distinct points in
, let be a family of homotopic classes Hi,i=1,..., j+m, of closed Jordan curves on, where the classes Hj+l, l=1,...,m, consist of curves that are homotopic to a point curve in b. Let =1,..., j+m be a system of positive numbers and letU be the modulus of the extremal-metric problem for the family and the system . In this paper we investigate the dependence of the modulusU=U(,A,B) on the parameters i and on the disposition of the points ak and b. One shows thatU is a smooth function of the indicated arguments and one obtains expressions for the derivatives
U,
U, and
U. One gives some applications of these results.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 72–82, 1985. 相似文献
20.
The largest Fischer 3-transposition group M(24) acts flag-transitively on a 3-local incidence geometry
(M(24)) which is a c-extension of the dual polar space associated with the group O
7(3). The action of the simple commutator subgroup M(24) is still flag-transitive. We show that
(M(24)) is characterized by its diagram under the flag-transitivity assumption. The result implies in particular that
(M(24)) is simply connected. The geometry
(M(24)) appears as a subgeometry in the Buekenhout-Fischer 3-local geometry
(F
1) of the Monster group. The simple connectedness of
(M(24)) has played a crucial role in the characterization of
(F
1), which has been achieved recently. When determining the possible structure of the parabolic subgroups we have used an unpublished pushing-up result by U. Meierfrankenfeld.Dedicated to Professor B. Fischer on the occasion of his sixtieth birthday 相似文献