Showing papers in "Journal of Geometry in 1998"
TL;DR: In this article, a negative answer to the questions raised by D.Blair-S.Ianus and A.Gray, respectively, of whether a compact almost Kahler manifold with Hermitian Ricci tensors belongs to the class AH2 is Kahler is given.
Abstract: We present a study of natural almost Hermitian structures on twistor spaces of quaternionic Kahler manifolds. This is used to supply (4n + 2)-dimensional examples (n > 1) of symplec tic non-Kahler manifolds. Studying their curvature properties we give a negative answer to the questions raised by D.Blair-S.Ianus and A.Gray, respectively, of whether a compact almost Kahler manifold with Hermitian Ricci tensor or whose curvature tensor belongs to the class AH2 is Kahler.
59 citations
TL;DR: In this article, the authors collect all results on the spectrum of values k that occur as the cardinality of a complete k-cap in a finite projective space, where k is the number of values in the spectrum.
Abstract: the aim of this paper is to collect all results on the spectrum of values k that occur as the cardinality of a complete k- cap in a finite projective space. 1
46 citations
TL;DR: In this paper, the authors consider the point-line geometries that arise as a shadow space in a spherical building with a diagram of type An, Bn, Cn, Dn or En, and determine in which cases the geometry is spanned by the set of points on an apartment.
Abstract: We consider the point-line geometries that arise as a shadow space in a spherical building with a diagram of type An, Bn, Cn, Dn or En, and determine in which cases the geometry is spanned by the set of points on an apartment. It turns out that this happens precisely in the cases corresponding to a minimal weight.
41 citations
40 citations
TL;DR: A block codeC is calledmetrically rigid, if every isometryφ: C→Fn with respect to theHamming metric is extendable to an isometry of the whole spaceFn.
Abstract: A block codeC
$$ \subseteq$$
F
n is calledmetrically rigid, if every isometryφ: C→F
n
with respect to theHamming metric is extendable to an isometry of the whole spaceF
n
. The metrical rigidity of some classes of codes is discussed.
30 citations
TL;DR: In this article, the authors give the classification of 3D contact metric manifolds satisfying νξτ = 0, which they have: harmonic curvature, or η-parralel Ricci tensor or cyclic ηparallel Ricci Tensor.
Abstract: We give the classification of the 3-dimensional contact metric manifolds satisfying ▽ξτ=0, which they have: harmonic curvature, or η-parralel Ricci tensor or cyclic η-parallel Ricci tensor.
24 citations
TL;DR: In this article, the authors define a generalized Jacobi operator on the Grassmanian of a curvature tensor and study when the characteristic polynomial of this operator is constant.
Abstract: Letg be a non-degenerate innerproduct of signature (p,q) onR m . LetGr r,s (g) be the Grassmanian of planes π so the restriction of g to π is non-degenerate and has signature (r, s). IfR is an algebraic curvature tensor onR m , we define a generalized Jacobi operator onGr r,s (g) and study when the characteristic polynomial of this operator is constant.
22 citations
TL;DR: The notion of O convexity is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected as discussed by the authors, which generalizes standard convexness as well as several other types of non traditional convexities.
Abstract: Restricted orientation convexity O convexity is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected The notion of O convexity generalizes standard convexity as well as several other types of non traditional convexity We introduce and study O halfspaces which are analogs of standard halfspaces in the theory of O convexity and directed O halfspaces which are restricted O halfspaces We explore some of the basic properties of them and outline their relationships to O convex sets and O connected sets which are restricted O convex sets in two and more dimensions For O halfspaces we prove that Every O halfspace is O convex if O has the point intersection property then the number of connected components of an O halfspace in d di mensions is at most d and this bound is attainable and the closed complement of an O halfspace is an O halfspace if and only if the boundary of the O halfspace is O convex In addition for directed O halfspaces we prove that Every O halfspace is O connected and the closed complement of a directed O halfspace is a directed O halfspace This research was supported by grants from the Natural Sciences and Engineering Research Council of Canada and from the Information Technology Research Centre of Ontario The Hong Kong University of Science Technology Technical Report Series Department of Computer Science
21 citations
TL;DR: In this article, the authors examine some geometric configurations of points in designs that give rise to vectors in the codes associated with the designs, and find vectors of small weight in the binary hull and in the code's orthogonal.
Abstract: We examine some geometric configurations of points in designs that give rise to vectors in the codes associated with the designs. In particular we look at small sets of points in projective planes of even order that are met evenly by all the lines of the plane, and find vectors of small weight in the binary hull and in the code's orthogonal.
14 citations
TL;DR: In this paper, non-Radon partition is used to partition convex hulls, and pseudoline arrangement is proposed to solve the problem of non-radon partitioning convex polygonal hulls.
Abstract: Keywords: non-Radon partition ; convex hull ; vertex ; pseudoline arrangement Note: PRO 98.11 Reference ROSO-ARTICLE-1998-001doi:10.1007/BF01237600 URL: http://dx.doi.org/10.1007/BF01237600 Record created on 2006-02-13, modified on 2016-08-08
12 citations
TL;DR: In this article, it was shown that it is possible to construct an equilateral triangle with given base in absolute planes, even if they satisfy bachmann'sLotschnittaxiom or the Archimedean axiom.
Abstract: It is shown, by indicating how to construct one with ruler and gauge, that there are equilateral triangles in absolutes planes which need not satisfy the circle axiom. However, it is not possible to construct an equilateral triangle with given base in absolute planes, even if they satisfy bachmann'sLotschnittaxiom or the Archimedean axiom.
TL;DR: In this paper, infinite elation generalized quadrangles as group coset geometries were discussed and the special case of those associated with flocks of quadratic cones of PG(3,K) was considered.
Abstract: We discuss infinite elation generalized quadrangles as group coset geometries and use this approach to deal with the special case of those associated with flocks of quadratic cones of PG(3,K).
TL;DR: In this article, the authors derived an isoperimetric inequality for timelike sectors in the Minkowski 2-spacetime space bounded by an achronal spacelike curve and two time-like rays from a point using Gauss-Bonnet formula.
Abstract: In the Minkowski 2-spacetime
$$\mathbb{L}^2 $$
the hyperbolic angle is defined by the hyperbolic parametrization of the plane. With this notion of hyperbolic angle Helzer obtained a relativistic version of Gauss-Bonnet formula (cf. [3]). In this paper, we derive an isoperimetric inequality for timelike sectors in
$$\mathbb{L}^2 $$
bounded by an achronal spacelike curve and two timelike rays from a point using this Gauss-Bonnet formula.
TL;DR: In this paper, the first examples of circle planes on the torus that are no Minkowski planes were constructed, but satisfy the same axiom of joining as flat Minkowowski planes.
Abstract: We construct first examples of circle planes on the torus that are no Minkowski planes, but satisfy the same axiom of joining as flat Minkowski planes. The circle planes constructed by us form a special class ofhyperbola structures (see [4]) or(B*)-Geometrien (see [2]).
TL;DR: In this paper, it was shown that isohedra with nonconvex faces must be starshaped and hence of genus 0, and that their faces are star-shaped pentagons with one concave vertex and that they are combinatorially equivalent to either the pentagonal dodecahedron, or to the polar of the snub cube or snub dodecahedral.
Abstract: An isohedron is a 3-dimensional polyhedron all faces of which are equivalent under symmetries of the polyhedron. Many well known polyhedra are isohedra; among them are the Platonic solids, the polars of Archimedean polyhedra, and a variety of polyhedra important in crystallography. Less well known are isohedra with nonconvex faces. We establish that such polyhedra must be starshaped and hence of genus 0, that their faces must be star-shaped pentagons with one concave vertex, and that they are combinatorially equivalent to either the pentagonal dodecahedron, or to the polar of the snub cube or snub dodecahedron.
TL;DR: Theorem 1 is a consequence of [3, Theorem 2.4] as discussed by the authors, which states that the set of points of n-dimensional hyperbolic geometry,n≥2.
Abstract: LetIn be the set of points ofn-dimensional hyperbolic geometry,n≥2. THEOREM 1. Letf∶In→In be a surjection such that images of hyperbolic lines are contained in hyperbolic lines. Thenf is a hyperbolic motion. THEOREM 2. Iff∶In→In maps hyperbolic lines onto hyperbolic lines, then the image off is a hyperbolic line, orf is a hyperbolic motion. We note that Theorem 1 is a consequence of [3, Theorem 2.4].
TL;DR: For a convex curve in an even-dimensional affine space, the authors introduced a series of convex domains (called Young hulls) which describe their structure and gave a formula for the volume of the biggest of these domains.
Abstract: For a convex curve in an even-dimensional affine space we introduce a series of convex domains (called Young hulls) describe their structure and give a formulas for the volume of the biggest of these domains.
TL;DR: In this paper, it was shown that every 3-τ-manifold with η-parallel Weyl tensor is either flat or a Sasakian manifold with constant curvature.
Abstract: Let M3 be a 3-dimensional contact metric manifold with contact structure (φ, ξ, η, g), such thatφ and l=R(.,ξ)ξ) commute. Such a manifold is called 3-τ-manifold. We prove that every 3-τ-manifold with η-parallel Weyl tensor is either flat or a Sasakian manifold with constant curvature 1.
TL;DR: A. The Construction==================¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ as discussed by the authors The General and Special Linear Groups====== ``(======¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¿¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯)
Abstract: A. The Construction
B. General and Special Linear Groups
C. Linear Groups over the Quaternions
D. Symplectic Groups
E. Pseudo-orthogonal and Pseudo-unitary Groups
F. Fibrations
TL;DR: In this article, the authors examined the geometric properties of the horizontal distribution on a manifold in terms of the affine connection defined by T. Y. Thomas, and showed that the choice of a particular affine connect in the projective class corresponds to the selection of an horizontal distribution.
Abstract: The bundle of volume forms on a manifold is examined in terms of the affine connection defined by T. Y. Thomas. The choice of a particular affine connection in the projective class corresponds to the choice of an horizontal distribution on this bundle. The geometric properties of the horizontal distributions are studied. Special lifts of vector fields and covariant tensor fields are examined as well as lifts of metric connections.
TL;DR: In this article, the Neuberg equation is used to describe the essential part of the locus of the scalene triangle in the plane for solving various locus problems with respect to scalene triangles.
Abstract: In this paper we explore various locus problems whose solutions involve the Neuberg cubic of the scalene triangle in the plane. We use analytical geometry to show that the Neuberg equation describes the essential part of the locus in each of these problems. In this way we discover new characteristics of the Neuberg cubic that has been at the focus of attention in the recent renaissance of triangle geometry.
TL;DR: In this article, it was shown that a theorem of miquelian type known as (M2) holds in a non-miquelians Laguerre plane of shear type as defined by Lowen and Pfuller.
Abstract: This note shows that a theorem of miquelian type known as (M2) holds in a certain non miquelian Laguerre plane of shear type as defined by Lowen and Pfuller[1].
TL;DR: In this paper, the problem of the compatibility and the equivalence of the tangency relations of sets of the classes A * p,k having the Darboux property at the pointp in generalized metric space (E,l) is considered.
Abstract: In this paper the problem of the compatibility and the equivalence of the tangency relations of sets of the classesA * p,k having the Darboux property at the pointp in generalized metric space (E,l) is considered. Some sufficient conditions for the compatibility and the equivalence of the tangency relations have been given here.
TL;DR: This is a story about an old problem of the outstanding French geometer J.D.Gergonne, about the answer to this problem which was widely accepted as correct (and rigorously proved) for many decades, but is in reality absolutely erroneous.
Abstract: This is a story about an old problem of the outstanding French geometer J.D.Gergonne. It is about the answer to this problem which was widely accepted as correct (and rigorously proved) for many decades, and cited as such in highly respected encyclopedias, but is in reality absolutely erroneous — the right answer is just the opposite. It is a story about two other problems closely related to that of Gergonne, about the possibility of finding highly plausible answers to them via computer experimentation.
TL;DR: In this paper, the authors introduce a web loop (P,\(\mathfrak{L}\), +) which is precisely a loop provided with the structure of a web such that both structures are compatible in the sense that for eacha ∈ P the map a+∶P→P;x↦a+x is an automorphism of (p,\(mathfrik{L}\)).
Abstract: We introduce a web loop (P,\(\mathfrak{L}\), +) which is precisely a loop (P,+) provided with the structure\(\mathfrak{L}\) of a web such that both structures are compatible in the sense that for eacha ∈P the map a+∶P→P;x↦a+x is an automorphism of (P,\(\mathfrak{L}\)). Exploiting the results of [6, 7, 9, Z] for the case of a web, we study web loops, webs with reflection structures and webs with point reflection structures.
TL;DR: In this paper, the weaker concept of contact spaces is used to characterize chain geometries instead of chain spaces possessing a distinguished automorphism group, which is the case in this paper.
Abstract: Chain geometries already were characterized by means of chain spaces possessing a distinguished automorphism group. Here instead of this the weaker concept of contact spaces is used.