共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Walter Benz 《Journal of Geometry》2004,79(1-2):27-30
This paper is concerned with the characterization of area-preserving mappings
of real inner product spaces. 相似文献
3.
Let E be a Euclidean space,
dim E 2. We say that
f : E
E preserves equilateral triangles if for all triples of
points x, y, z E
we have
We show that if E is a finite-dimensional Euclidean space,
dim E 2,
f:E
E is measurable and preserves
equilateral triangles, then it is a similarity transformation (an isometry
multiplied by a positive constant). Moreover, in spaces at least
three-dimensional we get a similarity transformation without any
regularity assumption. Some generalizations as well as some interesting examples are also
presented in the paper. 相似文献
4.
Discrete hyperbolic geometry 总被引:1,自引:0,他引:1
The aim of the paper is to make geometers and combinatorialists familiar with old and new connections between the geometry
of Lorentz space and combinatorics. Among the topics treated are equiangular lines and their relations to spherical 2-distance
sets; spherical and hyperbolic root systems and their relation to graphs whose second largest eigenvalue does not exceed one
or two, respectively; and work of Niemeier, Vinberg, Conway and Sloane on Euclidean and Lorentzian unimodular lattices.
The first author gratefully acknowledges the support of the Dutch organization for pure research, Z. W. O., during Sept.—Dec.
1980, thus allowing him to spend four months in Eindhoven (Netherlands). 相似文献
5.
Roland Höfer 《Aequationes Mathematicae》2006,71(1-2):162-173
6.
7.
Iosif Pinelis 《Journal of Geometry》2005,82(1-2):156-171
Let a1, ..., an be positive numbers satisfying the condition that each of the ai’s is less than the sum of the rest of them; this condition is necessary for the ai’s to be the edge lengths of a (closed) polygon. It is proved that then there exists a unique (up to an isometry) convex cyclic
polygon with edge lengths a1, ..., an. On the other hand, it is shown that, without the convexity condition, there is no uniqueness—even if the signs of all central
angles and the winding number are fixed, in addition to the edge lengths. 相似文献
8.
Wen-ling Huang 《Linear algebra and its applications》2011,435(1):175-185
We examine surjective maps which preserve a fixed bounded distance in both directions on some classical dual polar spaces. 相似文献
9.
Relationship between tetrahedron shape measures 总被引:6,自引:0,他引:6
Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle
min
theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form
wherec
0,c
1,e
0, ande
1 are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. 相似文献
10.
Mowaffaq Hajja 《Journal of Geometry》2005,83(1-2):46-56
In contrast with the analogous situation for a triangle, the cevians that join the vertices of a tetrahedron to the points
where the faces touch the insphere (or the exspheres) are not concurrent in general. This observation led the present author
and P. Walker in [4] to devise alternative definitions of the Gergonne and Nagel centers of a tetrahedron that do not assume
the concurrence of such cevians and that coincide with the ordinary definitions in the case of a triangle. They then proved
that the Gergonne center exists and is unique for all tetrahedra and that the Nagel center, though unique, exists only for
tetrahedra that satisfy certain conditions. In this article, we extend these definitions to simplices of any dimension. By
keeping the requirement that the Gergonne center be interior and relaxing such a condition for the Nagel center, we prove
that both centers exist and are unique for all simplices, thus polishing the definitions and generalizing the results of the
above-mentioned article. 相似文献
11.
Walter Benz 《Monatshefte für Mathematik》2004,141(1):1-10
The lines of euclidean and hyperbolic geometries are characterized as metric lines in the sense of Blumenthal–Menger, and the lines of spherical and elliptic geometry as periodic ones. In euclidean geometries there do not exist periodic lines. 相似文献
12.
13.
Robert D. Knight 《Journal of Geometry》2005,83(1-2):137-152
A simple classification of triples of Lie cycles is given. The class of each triad determines the number of solutions to the
associated oriented Apollonius contact problem. The classification is derived via 2-dimensional Lie contact geometry in the
form of two of its subgeometries—Laguerre geometry and oriented M?bius geometry. The method of proof illustrates interactions
between the two subgeometries of Lie geometry. Two models of Laguerre geometry are used: the classic model and the 3-dimensional
affine Minkowski space model. 相似文献
14.
Victor Pambuccian 《Aequationes Mathematicae》2003,66(1-2):90-99
15.
B. Ettaoui 《Geometriae Dedicata》1994,50(3):235-241
Résumé On montre l'existence, dans un espace projectif complexe, d'un tétraèdre régulier ayant un groupe de symétrie isomorphe à celui du tétraèdre régulier euclidien. On précise la classe d'homologie de dimension 2, qui contient le complexe simplicial qui lui est associé.
We show the existence, in a complex projective space, of a regular tetrahedron which has its symmetry group isomorphic to that of the euclidean regular tetrahedron. We give precisely the two-dimensional homology class, containing the simplicial complexe associated to it.相似文献
16.
We show that the shapes of convex bodies containing m translates of a convex body K, so that their Minkowskian surface area is minimum, tends for growing m to a convex body L.Received: 7 January 2002 相似文献
17.
We prove uncountably many new analytic and geometric isoperimetric inequalities associated with the solutions of second order ordinary differential equations. 相似文献
18.
Projective metrics were first introduced by A. Cayley and F. Klein who constructed analytical models over the field of complex numbers. The aim of this paper is to give for the first time a purely synthetic definition of all projective spaces with Cayley-Klein metrics and to develop the synthetic foundation of projective-metric geometry to a level of generality including metrics over arbitrary fields of characteristic 2. 相似文献
19.
Jan von Plato 《Annals of Pure and Applied Logic》2010,162(2):144-161
The axioms of projective and affine plane geometry are turned into rules of proof by which formal derivations are constructed. The rules act only on atomic formulas. It is shown that proof search for the derivability of atomic cases from atomic assumptions by these rules terminates (i.e., solves the word problem). This decision method is based on the central result of the combinatorial analysis of derivations by the geometric rules: The geometric objects that occur in derivations by the rules can be restricted to those known from the assumptions and cases. This “subterm property” is proved by permuting suitably the order of application of the geometric rules. As an example of the decision method, it is shown that there cannot exist a derivation of Euclid’s fifth postulate if the rule that corresponds to the uniqueness of the parallel line construction is taken away from the system of plane affine geometry. 相似文献
20.
Some years ago Caporaso and Harris have found a nice way to compute the numbers N(d, g) of complex plane curves of degree d and genus g through 3d + g − 1 general points with the help of relative Gromov-Witten invariants. Recently, Mikhalkin has found a way to reinterpret
the numbers N(d, g) in terms of tropical geometry and to compute them by counting certain lattice paths in integral polytopes. We relate these
two results by defining an analogue of the relative Gromov-Witten invariants and rederiving the Caporaso–Harris formula in
terms of both tropical geometry and lattice paths.
H. Markwig has been funded by the DFG grant Ga 636/2. 相似文献