Search results for "Affine geometry of curves"

showing 6 items of 6 documents

On the algebraic representation of projectively embeddable affine geometries

1995

The main result of this article is an application of [1] and [2] which yields that an at least 2-dimensional affine geometry is module-induced if and only if it is projectively embeddable into an Arguesian projective lattice geometry.

Affine geometryDiscrete mathematicsAffine geometry of curvesAlgebra representationGeometry and TopologyAffine transformationLattice (discrete subgroup)Affine planeMathematicsJournal of Geometry
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The coordinatization of affine planes by rings

1996

With every unitary free module of rank 2 there is naturally associated a generalized affine plane (e.g. the lines are just the cosets of all nonzero 1-generated submodules). Here we solve the converse problem by coordinatizing a given generalized affine plane which satisfies certain versions of Desargues' postulate.

Affine geometryAffine coordinate systemCombinatoricsAffine geometry of curvesAffine representationAffine hullAffine groupGeometry and TopologyAffine transformationAffine planeMathematicsGeometriae Dedicata
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On invariant measures of finite affine type tilings

2006

In this paper, we consider tilings of the hyperbolic 2-space, built with a finite number of polygonal tiles, up to affine transformation. To such a tiling T, we associate a space of tilings: the continuous hull Omega(T) on which the affine group acts. This space Omega(T) inherits a solenoid structure whose leaves correspond to the orbits of the affine group. First we prove the finite harmonic measures of this laminated space correspond to finite invariant measures for the affine group action. Then we give a complete combinatorial description of these finite invariant measures. Finally we give examples with an arbitrary number of ergodic invariant probability measures.

General MathematicsSubstitution tiling[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]30C85Dynamical Systems (math.DS)01 natural sciences37D40; 52C20; 30C85CombinatoricsAffine geometryAffine representationAffine hull0103 physical sciencesAffine groupFOS: MathematicsMathematics - Dynamical Systems0101 mathematicsMathematics37D40Applied Mathematics010102 general mathematics52C20Affine coordinate systemAffine shape adaptationAffine geometry of curves010307 mathematical physics
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An axiomatic treatment of ratios in an affine plane

1967

Affine geometryPure mathematicsAffine geometry of curvesPlane curveGeneral MathematicsAffine groupAffine spaceAffine planeAxiomMathematicsArchiv der Mathematik
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Affine Kettengeometrien �ber Jordanalgebren

1996

It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.

Affine coordinate systemDiscrete mathematicsAffine geometryQuantum affine algebraPure mathematicsAffine representationAffine geometry of curvesAffine hullAffine groupGeometry and TopologyAffine planeMathematicsGeometriae Dedicata
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Symplectic Applicability of Lagrangian Surfaces

2009

We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equa- tions. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.

Mathematics - Differential GeometryPure mathematicsdifferential invariantsSymplectic vector spaceFOS: MathematicsSymplectomorphismMoment mapMathematics::Symplectic GeometryMathematical PhysicsMathematicsSymplectic manifoldapplicabilityLagrangian surfaceslcsh:MathematicsMathematical analysisSymplectic representationmoving frameslcsh:QA1-939Symplectic matrixaffine symplectic geometryAffine geometry of curvesDifferential Geometry (math.DG)Lagrangian surfaces; affine symplectic geometry; moving frames; differential invariants; applicability.Geometry and TopologyAnalysisSymplectic geometry
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