Journal of Geometry

article

A new proof of the existence of (q ²−q + 1)-arcs inpg(2, q²)

Antonio Cossidente

Journal of Geometry > 1997 > 59 > 1-2 > 32-33

Research performed within the activity of G.N.S.A.G.A. of C.N.R. with the support of the Italian Ministry for Research and Technology

article

On generalized projective spaces operating on sets

Johannes André

Journal of Geometry > 1998 > 62 > 1-2 > 200-200

article

Antimatroids of finite character

Nathalie Wahl

Journal of Geometry > 2001 > 70 > 1-2 > 168-175

Abstract.We give an axiomatisation of antimatroids of finite character through compatible orderings. P.H. Edeleman and R.E. Jamison show that, in the finite case, the building blocks of antimatroids are in some sense their compatible orderings. We propose a definition of antimatroids for the general case justified by an extension of their result to the infinite case. This implies a study of maximal...

article

Harmonic mappings and hyperbolic Plcker transformations

Klaus List

Journal of Geometry > 2001 > 70 > 1-2 > 108-116

Abstract. Let $\Pi_h$ be a 3-dimensional hyperbolic space with Euclidean ground field $\Bbb K$ . There is a certain procedure by which any harmonic mapping of the projective line over the unique quadratic extension of $\Bbb K$ induces an orthogonality-preserving Plcker transformation of $\Pi_h$ and, conversely, any orthogonality-preserving Plcker transformation of $\Pi_h$ is induced by such a...

article

Congruence theorem for 4-tuples in the Grassmann manifold $G_2(R^8)$

Giovanni Masala

Journal of Geometry > 2001 > 70 > 1-2 > 117-132

Abstract. We give a complete set of orthogonal invariants for tetrahedra in $G_2(R^8)$ . As a consequence, we characterise regular tetrahedra and we exhibit the existence regions of these objects in comparison with the angular invariants associated to them.

article

Mappings preserving two hyperbolic distances

Walter Benz Hamburg

Journal of Geometry > 2001 > 70 > 1-2 > 8-16

Abstract. Suppose that X is the set of points of a hyperbolic geometry of finite or infinite dimension $\geq2$ , and that $\varrho0$ is a fixed real number and N1 a fixed integer. Let $f:X\to X$ be a mapping such that for every $x,y\in X$ if h(x, y)= $\varrho$ , then h(f,(x),f,(y)) $\leq\varrho$ , and if h(x,y) = N $\varrho$ , then h(f,(x),f,(y)) $\geq N\varrho$ , where h,(p,q) designates the hyperbolic...

article

Self-intersections and smoothness of general offset surfaces

Johannes Wallner

Journal of Geometry > 2001 > 70 > 1-2 > 176-190

Abstract. A convex body N moves such that it touches a closed surface M. While doing this, it is undergoing a purely translational motion. A fixed point of N traces out the general offset surface $\gamma$ during this motion. We study the connection between singularities and self-intersections of $\gamma$ and the possible collisions of M with N during this motion and obtain some global results.

article

Intersection of maximal orthogonally starshaped polygons

Oleg Topal

Journal of Geometry > 2001 > 70 > 1-2 > 164-167

Abstract. Let S be a simply connected orthogonal polygon in $R^2$ and let P(S) denote the intersection of all maximal starshaped via staircase paths orthogonal subpolygons in S. Our result: if $P(S)\ne \emptyset$ , then there exists a maximal starshaped via staircase paths orthogonal polygon $T\subseteq S$ , such that $KerT\subseteq KerP(S)$ . As a corollary, P(S) is a starshaped (via staircase paths)...

article

Conformally flat contact metric manifolds

Amalendu Ghosh, Themis Koufogiorgos, Ramesh Sharma

Journal of Geometry > 2001 > 70 > 1-2 > 66-76

Abstract. A couple of classes of conformally flat contact metric manifolds have been classified. Conformally flat contact manifolds have been characterized as hypersurfaces of 4-dimensional Kaehler Einstein (in particular, Calabi-Yau) manifolds.

article

Axioms of planes on real hypersurfaces in complex space forms

Miguel Ortega

Journal of Geometry > 2001 > 70 > 1-2 > 139-150

Abstract. A Riemannian manifold M satisfies the axiom of 2-planes if at each point $p\in{M}$ and each tangent 2-plane V at the point, there exists a totally geodesic submanifold L with $p\in{L}$ and $T_pL=V$ . On the other hand, real hypersurfaces in complex space forms have nice families of tangent 2-planes. If we restrict the above definition to those planes, several definitions of axioms of 2-planes...

article

Finite Minkowski planes and embedded inversive planes

Gloria Rinaldi

Journal of Geometry > 2001 > 70 > 1-2 > 160-163

Abstract. We show that each known finite Minkowski plane of order $p^m,m$ even, contains embedded Miquelian inversive planes, (cf. Proposition 1).

article

An extension of Harveys formula

Robert J. Gregorac

Journal of Geometry > 2001 > 70 > 1-2 > 77-84

Abstract. We generalize Harveys formula from n+2 spheres orthogonal to a sphere in $R^n$ to any $m\ge n+2$ points in $R^n$ .

article

Generalising a characterisation of Hermitian curves

S. G. Barwick, Catherine T. Quinn

Journal of Geometry > 2001 > 70 > 1-2 > 1-7

Abstract. This article proves a characterisation of the classical unital that is a generalisation of a characterisation proved in 1982 by Lefvre-Percsy. It is shown that if ${\cal U}$ is a Buekenhout-Metz unital with respect to a line $\ell_\infty$ in $PG(2,q^2)$ such that a line of $PG(2,q^2)$ not through $\cal U cap \ell_\infty$ meets ${\cal U}$ in a Baer subline, then ${\cal U}$ is classical...

article

On finite {s-2, s}-semiaffine linear spaces

Nicola Durante

Journal of Geometry > 2001 > 70 > 1-2 > 44-58

Abstract. In this paper finite {s-2, s}-semiaffine linear spaces of order n are studied. It is proved that if s= 6 or $s\ge 8$ then there is only a finite number of such linear spaces.

article

A note on the Fermat-Torricelli point of a d-simplex

Leoni Dalla

Journal of Geometry > 2001 > 70 > 1-2 > 38-43

Abstract. The isogonal property of the Fermat-Torricelli point for the vertex set of a d-simplex is examined. For d=2 and 3, it is known that the property holds true if the point is in the interior of the simplex, but for $d \geq 4$ an example is given, proving that the Fermat-Torricelli point is not necessarily isogonal.

article

Unitary polarities in non commutative twisted field planes

Eliana Francot

Journal of Geometry > 2001 > 70 > 1-2 > 59-65

Abstract. In this paper the class of polarities in non commutative twisted field planes, defined in a paper of Biliotti, Jha and Johnson ([4]), is investigated. It is proved that these polarities are unitary and that the associated unitals have a collineation group that fixes a point and is transitive on the remaining ones.

article

Dihedral groups generated by Baer involutions in $\rm P \Gamma \rm L(3,q^2)$

Harm Pralle, Johannes Ueberberg

Journal of Geometry > 2001 > 70 > 1-2 > 151-159

Abstract. The product $\delta =\tau \tau ^{\prime }$ of two Baer involutions $\tau,\tau ^{\prime }\in \mathrm{P}\Gamma \mathrm{L}(3,q^2)$ is the rotation of the dihedral group $\cal D =\langle \tau ,\tau ^{\prime}\rangle$ . It is a projectivity. The properties of $\delta$ are closely related to the intersection configuration of the two corresponding Baer subplanes B and $B^{\prime}$ , resp. In...

article

Submanifolds with pointwise planar normal sections in a sphere

Shi-jie Li

Journal of Geometry > 2001 > 70 > 1-2 > 101-107

Abstract. In this article, we prove that a submanifold of $S^m$ has pointwise 2- or 3-planar normal sections via the second standard immersion of $S^m$ if and only if it is totally geodesic in $S^m$ .

article

Two-transitive parabolic ovals

Mauro Biliotti, Vikram Jha, Norman L. Johnson

Journal of Geometry > 2001 > 70 > 1-2 > 17-27

Abstract. We investigate finite affine planes $\pi$ of even order possessing a parabolic oval $\Omega (\left| \Omega \cap l_{\infty }\right| =1)$ and a collineation group G which leaves $\Omega$ invariant and acts 2-transitively on its affine points. The main attention is devoted to translation planes. The odd order case has already been considered by Enea and Korchmaros in [5]. Our main result...

article

Projectively flat affine surfaces with flat affine metric

Chaujun Isaac Lee, Luc Vrancken

Journal of Geometry > 2001 > 70 > 1-2 > 85-100

Abstract. We completely classify affine surfaces with projectively flat induced connection and flat affine metric.

INFONA - science communication portal

Journal of Geometry

A new proof of the existence of (q ²−q + 1)-arcs inpg(2, q²)

On generalized projective spaces operating on sets

Antimatroids of finite character

Harmonic mappings and hyperbolic Plcker transformations

Congruence theorem for 4-tuples in the Grassmann manifold $G_2(R^8)$

Mappings preserving two hyperbolic distances

Self-intersections and smoothness of general offset surfaces

Intersection of maximal orthogonally starshaped polygons

Conformally flat contact metric manifolds

Axioms of planes on real hypersurfaces in complex space forms

Finite Minkowski planes and embedded inversive planes

An extension of Harveys formula

Generalising a characterisation of Hermitian curves

On finite {s-2, s}-semiaffine linear spaces

A note on the Fermat-Torricelli point of a d-simplex

Unitary polarities in non commutative twisted field planes

Dihedral groups generated by Baer involutions in $\rm P \Gamma \rm L(3,q^2)$

Submanifolds with pointwise planar normal sections in a sphere

Two-transitive parabolic ovals

Projectively flat affine surfaces with flat affine metric

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