共查询到20条相似文献,搜索用时 11 毫秒
1.
Thomas Ivey 《Geometriae Dedicata》1997,64(2):125-144
The Pick cubic form is a fundamental invariant in the (equi)affine differential geometry of hypersurfaces. We study its role in the affine isometric embedding problem, using exterior differential systems (EDS). We give pointwise conditions on the Pick form under which an isometric embedding of a Riemannian manifold M
3 into
is rigid. The role of the Pick form in the characteristic variety of the EDS leads us to write down examples of nonrigid isometric embeddings for a class of warped product M
3's. 相似文献
2.
Let be a regular near polygon of order (s,t) with s>1 and t3. Let d be the diameter of , and let r:= max{i(ci,ai,bi)=(c1,a1,b1)}. In this note we prove several inequalities for . In particular, we show that s is bounded from above by function in t if We also consider regular near polygons of order (s,3).This work was partly supported by the Grant-in-Aid for Scientific Research (No 14740072), the Ministry of Education, Culture, Sports, Science and Technology, JapanThis work was partly done when the author was at the Com2MaC center at the Pohang University of Science and Technology. He would like to thank the Com2MaC-KOSEF for its support 相似文献
3.
We construct a nondegenerate near polygon from a partial linear space without isolated points. We also prove that the points of a near polygon at distance at most 2 from a fixed point induce a near polygon, which is related to the class of the near polygons obtained from the construction. We give also a characterization of the near polygons of Hamming type in terms of parallelism. 相似文献
4.
In this note we will generalize the Higman-Haemers inequalities for generalized polygons to thick regular near polygons. 相似文献
5.
Bart De Bruyn 《Journal of Algebraic Combinatorics》2003,18(1):41-46
Let S be a near polygon of order (s, t) with quads through every two points at distance 2. The near polygon S is called semifinite if exactly one of s and t is finite. We show that S cannot be semifinite if s = 2 and derive upper bounds for t. 相似文献
6.
In this note we classify the regular near polygons of order (s, 2). 相似文献
7.
In this paper we initiate the study of hybrid slim near hexagons. These are near hexagons which are not dense and not a generalized hexagon in which each line is incident with exactly three points. In the present paper, we will emphasize slim near hexagons with at least one W(2)-quad or Q(5, 2)-quad. Such near hexagons are finite if there are no special points, i.e. points which lie at distance at most 2 from any other point. We will determine upper bounds for the number of lines through a fixed point. We will also look at the special case where the near hexagon has an order. We will determine all slim near hexagons with an order which contain at least one (necessarily big) Q(5,2)-quad, or at least one big W(2)-quad.AMS Classification 05B25, 51E12Communicated by: M.J. de ResminiPostdoctoral Fellow of the Research Foundation–Flanders. 相似文献
8.
Bart De Bruyn 《Journal of Algebraic Combinatorics》2000,11(3):211-226
The glueing-construction described in this paper makes use of two generalized quadrangles with a spread in each of them and yields a partial linear space with special properties. We study the conditions under which glueing will give a near hexagon. These near hexagons satisfy the nice property that every two points at distance 2 are contained in a quad. We characterize the class of the glued near hexagons and give examples, some of which are new near hexagons. 相似文献
9.
10.
From an elementary observation, we derive some upper bounds for the number of mutually opposite points in the classical generalized polygons having 3 points on each line. In particular, it follows that the Ree-Tits generalized octagon O(2) of order (2, 4) has no ovoids. Also, we deduce from another observation a similar upper bound in any generalized hexagon of order (s, s
3). 相似文献
11.
Oliver Baues 《Geometriae Dedicata》1999,75(1):33-56
Affine structures on surfaces are constructed by gluing polygons. The geometry of the affine surface depends on the shape of the polygon(s) and the particular gluing transformations used. The affine version of the Poincaré fundamental polygon theorem expresses the fundamental group and holonomy of the surface in terms of the gluing data. The theorem may be used to construct all complete affine structures on the 2-torus. The space of inequivalent holonomy representations of such structures is homeomorphic to R2. 相似文献
12.
We determine all distance-2-sets and all valuations of the 11 slim dense near hexagons. We consider this as a necessary step
in order to classify all slim dense near octagons. These near octagons will be classified in a forthcoming paper.
Received November 29, 2004 相似文献
13.
Thomas Ivey 《Geometriae Dedicata》1999,75(3):235-243
A strictly convex hypersurface in Rn can be endowed with a Riemannian metric in a way that is invariant under the group of (equi)affine motions. We study the corresponding isometric embedding problem for surfaces in R3. This problem is formulated in terms of a quasilinear elliptic system of PDE for the Pick form. A negative result is obtained by attempting to invert about the standard embedding of the round sphere as an ellipsoid. 相似文献
14.
Vincent Borrelli 《Annals of Global Analysis and Geometry》1999,17(4):371-384
Given a totally real embedding j of the 2-torus
into 2, one defines a 1-class 1 – its linking class – which is a tool to detect arcwise connected components of the space of totally real embeddings EmbTr(
, 2). We generalize the construction of the linking class to any totally real embedding j of a connected, oriented, compact manifold without boundary M
n
into n. We obtain an (n – 1)-class
n– 1 which is still an invariant for isotopy classes of totally real embeddings. We show that this class is nontrivial by computing it for some families of totally real embeddings. We then study the relationship between isotopy classes of ordinary embeddings and the linking class. With additional assumptions on M
n
(n 4 and M
n
parallelizable) we obtain the following: two totally real embeddings of M
n
into
n
which belong to the same isotopy class of totally real immersion, belong to the same isotopy class of ordinary embedding if and only if (1) their linking classes are the same (if n odd); (2) the images of their linking classes by the coefficient homomorphism : H
n– 1 (M
n
, ) H
n– 1 (M
n
, 2) are the same (if n even). 相似文献
15.
研究了不可定向曲面上最大亏格嵌入的估计数,得到了几类图的指数级不可定向最大亏格嵌入的估计数的下界.利用电流图理论,证明了完全图K_(12s)在不可定向曲面上至少有2~(3s-1)个最小亏格嵌入;完全图K_(12s+3)在不可定向曲面上至少有2~(2s)个最小亏格嵌入;完全图K_(12s+7)在不可定向曲面上至少有2~(2s+1)个最小亏格嵌入. 相似文献
16.
We prove that the Veronese embedding
O
n
(d):
n
N
with n2, d3 does not satisfy property N
p (according to Green and Lazarsfeld) if p3d–2. We make the conjecture that also the converse holds. This is true for n=2 and for n=d=3. 相似文献
17.
Vladimir P. Korzhik 《Journal of Graph Theory》2013,74(2):133-142
We construct (resp. ) index one current graphs with current group such that the current graphs have different underlying graphs and generate nonisomorphic orientable (resp. nonorientable) quadrangular embeddings of the complete graph , (resp. ). 相似文献
18.
设Γ是直径为d且型为(α 1,3)的距离正则图,其中α≥2.用l(c,a,b)表示交叉阵列l(Γ)中列(c,a,b)~t的个数,记r=r(Γ)=l(c_1,a_1,b_1),s=s(Γ)=l(c_(r 1),a(r 1),b_(r 1)).那末,若c_(r 1)=3且a_(r 1)=3a,则d=r s 1,c_d=4且Γ为正则拟2d边形. 相似文献
19.
LiuYING LiuYANPEI 《高校应用数学学报(英文版)》1997,12(3):253-258
The purpose of this paper is to display a new kind of simple graphs which belong to B. inwhich any graph has its orientable genus n,n≥3. Furthermore, for any integer k,1≤k≤n,there exists a graph B^kn of B. such that the non-orientable genus of B^kn is k. 相似文献
20.
Let
, n ≥ 2, be the near 2n-gon on the 2-factors of a complete graph with 2n + 2 vertices. In this paper, we classify the valuations of the near octagon
. We use this classification to study isometric full embeddings of
into DQ(8,2) and DH(7,4). We show that there is up to isomorphism a unique isometric full embedding of
into each of these dual polar spaces. Further applications are expected in the classification of dense near polygons with
lines of size 3. 相似文献