共查询到20条相似文献,搜索用时 31 毫秒
1.
Stefan Immervoll 《Archiv der Mathematik》2009,92(2):184-190
In [5] and [6] we proved that (non-empty) sets of absolute points of smooth polarities, i.e. smooth polar unitals, in smooth
projective planes of dimension 2l are smooth submanifolds of the point spaces homeomorphic to spheres of dimension . In this paper we show that the intersections of smooth polar unitals with secants are homeomorphic to spheres of dimension
, respectively. Furthermore we prove that the condition of connectedness in [6, Theorem 1.2] may be omitted. This means that
a closed (not necessarily connected) submanifold U of the point space of a smooth projective plane is homeomorphic to a sphere provided that there exists precisely one tangent
at each point of U, and each secant intersects U transversally. If U has codimension 1 in the point space then the second condition follows from the first one, and also the intersections of
U with secants are homeomorphic to spheres. This result may be generalized to compact hypersurfaces in the point spaces of
smooth affine planes.
Received: 1 July 2008 相似文献
2.
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
3.
We show that a closed simply connected 8-manifold (9-manifold) of positive sectional curvature on which a 3-torus (4-torus) acts isometrically is homeomorphic to a sphere, a complex projective space or a quaternionic projective plane (sphere). We show that a closed simply connected 2m-manifold (m5) of positive sectional curvature on which an (m–1)-torus acts isometrically is homeomorphic to a complex projective space if and only if its Euler characteristic is not 2. By [Wi], these results imply a homeomorphism classification for positively curved n-manifolds (n8) of almost maximal symmetry rank Supported by CNPq of Brazil, NSFC Grant 19741002, RFDP and Qiu-Shi Foundation of China.Supported partially by NSF Grant DMS 0203164 and a research grant from Capital normal university. 相似文献
4.
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
5.
In this paper we introduce and analyze the notion of self-dual
k-sets of type (m, n).
We show that in a non-square order projective space such sets exist
only if the dimension is odd. We prove that, in a projective space of odd dimension
and order q, self-dual
k-sets of type (m, n), with
, are of elliptic and hyperbolic
type, respectively. As a corollary we obtain a new characterization of the
non-singular elliptic and hyperbolic quadrics. 相似文献
6.
This paper studies the cardinality of a smallest set
of t-subspaces of the finite projective spaces PG(n, q) such that every s-subspace is incident with at least one element of
, where 0 t < s n. This is a very difficult problem and the solution is known only for very few families of triples (s, t, n). When the answer is known, the corresponding blocking configurations usually are partitions of a subspace of PG(n, q) by subspaces of dimension t. One of the exceptions is the solution in the case t = 1 and n = 2s. In this paper, we solve the case when t = 1 and 2s < n 3s-3 and q is sufficiently large. 相似文献
7.
We investigate finite translation planes of odd dimension over their kernels in which the translation complement induces on each component l a permutation group whose order is divisible by a p-primitive divisor. Using results of this investigation, we show that rank 3 affine planes of odd dimension over their kernels are either generalized André planes or semi-field planes. A similar result is given for translation planes having a collineation group which is doubly transitive on each affine line; besides the above two possibilities, there is a third possibility; the plane has order 27, the translation complement is doubly transitive on
, and SL(2, 13) is contained in the translation complement.We also consider translation planes of odd dimension over their kernels which have a collineation group isomorphic to SL(2, w) with w prime to 5 and the characteristic, and having no affine perspectivity. We show that such planes have order 27, the prime power w=13, and the given group together with the translations forms a doubly transitive collineation group on {ie153-1}. This indicates quite strongly that the Hering translation plane of order 27 is unique with respect to the above properties.Both authors supported in part by NSF Grant No. MCS76-0661 A01. 相似文献
8.
Klaus-Dieter Kirchberg 《Annals of Global Analysis and Geometry》1993,11(2):141-164
In the paper Kählerian Killing spinors are defined and their basic properties are investigated. Each Kähler manifold that admits a Kählerian Killing spinor is Einstein of odd complex dimension. Kählerian Killing spinors are a special kind of Kählerian twistor spinors. Real Kählerian Killing spinors appear for example, on closed Kähler manifolds with the smallest possible first eigenvalue of the Dirac operator. For the complex projective spaces
P
2l–1 and the complex hyperbolic spaces
H
2l–1 withl>1 the dimension of the space of Kählerian Killing spinors is equal to (
). It is shown that in complex dimension 3 the complex hyperbolic space
H
3 is the only simple connected complete spin Kähler manifold admitting an imaginary Kählerian Killing spinor. 相似文献
9.
Chihiro Suetake 《Geometriae Dedicata》1994,51(2):123-131
Let be a translation plane of orderq
3,q an odd prime power, whose kern GF(q). Letl
be the line at infinity of . LetG be a solvable collineation group of in the linear translation complement, which acts transitively onl
, and letH be a maximal normal cyclic subgroup ofG. Then the restriction
ofH onl
acts semiregularly onl
and
{1, 2, 3, 6}, where
is the restriction ofG onl
(ifq –1(mod 3), then
{1, 2}). Ifq {3, 5} and
{1, 2}, then is determined completely, using a computer. 相似文献
10.
Let X be a smooth complex projective variety and let
be
a smooth submanifold of dimension
, which is the zero
locus of a section of an ample vector bundle
of rank
on X. Let H be an ample line bundle
on X, whose restriction
HZ to Z is generated by global sections.
Triplets
as above are classified under the
assumption that
is a polarized manifold of sectional genus
2. This can be regarded as a step towards the classification of ample
vector bundles of corank one and curve genus two.
Received: 6 June 2003 相似文献
11.
ATSUSHI NOMA 《Compositio Mathematica》1997,106(1):61-70
For a smooth projective variety X of dimension n in a projective space
defined over an algebraically closed field k, the Gauss mapis a morphism from X to the Grassmannian of n-plans in
sending
to the embedded tangent space
.The purpose of this paper is to prove the generic injectivity of Gauss mapsin positive characteristic for two cases; (1) weighted complete intersectionsof dimension
of general type; (2) surfaces or 3-folds with -semistable tangent bundles; based on a criterion of Kaji by looking atthe stability of Frobenius pull-backs of their tangent bundles. The first result implies that a conjecture of Kleiman--Piene is true in case X is of general type of dimension
. The second result is a generalization of the injectivity for curves. 相似文献
12.
Walter Benz 《Journal of Geometry》2004,79(1-2):19-26
Suppose that X is a real inner product
space of (finite or infinite) dimension at least 2. A distance preserving mapping
, where
is a (finite or infinite) subset of a
finite-dimensional subspace of X, can be extended
to an isometry
of X. This holds true for
euclidean as well as for hyperbolic geometry. To both geometries there exist examples
of non-extentable distance preserving
, where S
is not contained in a finite-dimensional subspace of
X. 相似文献
13.
Richard Bödi 《Geometriae Dedicata》1998,72(3):283-297
Smooth projective planes are projective planes defined on smooth manifolds (i.e. the set of points and the set of lines are smooth manifolds) such that the geometric operations of join and intersection are smooth. A systematic study of such planes and of their collineation groups can be found in previous works of the author. We prove in this paper that a 16-dimensional smooth projective plane which admits a collineation group of dimension d 39 is isomorphic to the octonion projective plane P2 O. For topological compact projective planes this is true if d 41. Note that there are nonclassical topological planes with a collineation group of dimension 40. 相似文献
14.
Let M be a compact oriented minimal
hypersurface of the unit n-dimensional sphere
Sn.
It is known that if the norm squared of the second fundamental form,
, satisfies that
for all
, then M is isometric to a Clifford
minimal hypersurface ([2], [5]). In this paper we will generalize this result
for minimal hypersurfaces with two principal curvatures and dimension greater
than 2. For these hypersurfaces we will show that if the average of the function
is n - 1, then M
must be a Clifford hypersurface.
Received: 24 December 2002 相似文献
15.
Mark Pankov 《Journal of Geometry》2004,79(1-2):169-176
Let
be a finite-dimensional projective space
and
be the Grassmannian consisting of
all k-dimensional subspaces of
. In the paper we show that
transformations of
sending base subsets
to base subsets are induced by collineations of
to itself or to the dual projective space
.
This statement generalizes the main result of the authors paper [19]. 相似文献
16.
Tamás Szőnyi 《Combinatorica》1992,12(2):227-235
A subsetS of a finite projective plane of orderq is called a blocking set ifS meets every line but contains no line. For the size of an inclusion-minimal blocking setq+
+Sq
+1 holds ([6]). Ifq is a square, then inPG(2,q) there are minimal blocking sets with cardinalityq
+1. Ifq is not a square, then the various constructions known to the author yield minimal blocking sets with less than 3q points. In the present note we show that inPG(2,q),q1 (mod 4) there are minimal blocking sets having more thanqlog2
q/2 points. The blocking sets constructed in this note contain the union ofk conics, whereklog2
q/2. A slight modification of the construction works forq3 (mod 4) and gives the existence of minimal blocking sets of sizecqlog2
q for some constantc.As a by-product we construct minimal blocking sets of cardinalityq
+1, i.e. unitals, in Galois planes of square order. Since these unitals can be obtained as the union of
parabolas, they are not classical. 相似文献
17.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献
18.
The purpose here is to show that an irreducible, reduced, projective,
nonhyperelliptic curve of degree d and
genus g is n-regular for
if
Received: 10 July 2003 相似文献
19.
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
20.
In this note we prove the uniqueness of U in a group G with
a spherical split-BN-pair of rank
,i.e., if G has such a BN-pair with
a nilpotent normal subgroup of B,
and
, then
and
is a normal subgroup of G. Here
is the corresponding group of Lie-type and
the subgroup of
generated by all root-subgroups corresponding to positive roots.
Received: 19 May 2003 相似文献