Results 1 to 10 of about 37,802 (311)
METHODOLOGICAL APPROACH TO CONGRUENCE OF QUADRILATERALS IN HYPERBOLIC GEOMETRY
Facta Universitatis. Series, Teaching, Learning and Teacher Education, 2021 In this paper we will prove new criteria for the congruence of convex quadrilaterals in Hyperbolic geometry and consequently, display the appropriate methodological approach in teaching the same.
Milan Zlatanović, Victor Aguilar
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Discrete asymptotic nets and W-congruences in Plücker line geometry [PDF]
Journal of Geometry and Physics, 2001 The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric.
Adam Doliwa
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Lorentzian manifolds with shearfree congruences and K\\"ahler-Sasaki\n geometry [PDF]
Differential Geometry and its Applications, 2020 We study Lorentzian manifolds $(M, g)$ of dimension $n\geq 4$, equipped with a maximally twisting shearfree null vector field $p_o$, for which the leaf space $S = M/\{\exp t p_o\}$ is a smooth manifold. If $n = 2k$, the quotient $S = M/\{\exp t p_o\}$ is naturally equipped with a subconformal structure of contact type and, in the most interesting cases,
Dmitri V. Alekseevsky +3 more
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On the geometry of spacelike congruences
Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2001 The authors consider the Blaschke trihedron and the Blaschke vectors of a timelike or a spacelike ruled surface in a Lorentzian space. Then, using duality properties, they obtain two fundamental formulae between Blaschke vectors of an arbitrary spacelike (or timelike) ruled surface and the parameter ruled surfaces passing through a straight line of a ...
Özkan Kılıç +2 more
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On the affine geometry of congruences of lines [PDF]
, 2023 Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of co-ordinates, for example that associated with their focal sets, and less well studied focal planes.
J. W. Bruce, Farid Tari
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Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry [PDF]
Journal of Non-linear Mathematical Physics, 2001 This paper is devoted to asymptotic lattices and \(W\)-congruences in integrable discrete geometry. First the author collects basic results of the Plücker line geometry that provide the appropriate setting for the subsequent discussion of geometric properties of asymptotic nets and \(W\)-congruences.
Adam Doliwa
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Sequences of enumerative geometry: congruences and asymptotics [PDF]
Experimental Mathematics, 2006 We study the integer sequence v_n of numbers of lines in hypersurfaces of degree 2n-3 of P^n, n>1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the v_n are described (in an appendix by Don Zagier).
Daniel B. Grünberg, Pieter Moree
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Congruences and Concurrent Lines in Multi-View Geometry [PDF]
Advances in Applied Mathematics, 2016 We present a new framework for multi-view geometry in computer vision. A camera is a mapping between $\mathbb{P}^3$ and a line congruence. This model, which ignores image planes and measurements, is a natural abstraction of traditional pinhole cameras. It includes two-slit cameras, pushbroom cameras, catadioptric cameras, and many more.
Juliana Rubio Ponce +2 more
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The topological shadow of F1-geometry: congruence spaces [PDF]
Mathematische zeitschrift, 2023 52 ...
Oliver Lorscheid, Samarpita Ray
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Intrinsic geometry of oriented congruences in three dimensions [PDF]
Journal of Geometry and Physics, 2008 Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in $R^3$, we abstract the notion of an oriented congruence structure. This is a 3-dimensional CR manifold $(M,H, J)$ with a preferred splitting of the tangent space $TM=V\oplus H$. We find all local invariants of such structures using Cartan's equivalence
C. Denson Hill, Paweł Nurowski
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