Results 11 to 20 of about 37,514 (226)
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 ...
KILIÇ, OSMAN +2 more
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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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Congruences and concurrent lines in multi-view geometry [PDF]
Advances in Applied Mathematics, 2017 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.
J. Ponce, B. Sturmfels, and M. Trager
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Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry [PDF]
Journal of pure and applied algebra, 2023 We introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its strong congruence space and the complex toric variety associated to its fan have the same dimension.
Manoel Jarra
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Mirror symmetry and projective geometry of Reye congruences I [PDF]
Journal of Algebraic Geometry, 2013 Studying the mirror symmetry of a Calabi-Yau threefold X X of the Reye congruence in P 4 \mathbb {P}^4 , we conjecture that X X has a non-trivial Fourier-Mukai partner Y Y .
Hosono, Shinobu, Takagi, Hiromichi
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Sequences of enumerative geometry: congruences and asymptotics [PDF]
, 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).
Grunberg, Daniel B., Moree, Pieter
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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.
Bruce, J. W., Tari, F.
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Intrinsic geometry of oriented congruences in three dimensions [PDF]
Journal of Geometry and Physics, 2009 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
Hill, C. Denson, Nurowski, Paweł
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The topological shadow of F1-geometry: congruence spaces [PDF]
Mathematische zeitschrift, 2023 52 ...
Lorscheid, Oliver, Ray, Samarpita
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Evolution of inhomogeneous LTB geometry with tilted congruence and modified gravity [PDF]
Canadian Journal of Physics, 2017 The goal of this paper is to shed some light on the significance of congruence of observers, which seems to affect the dynamics of the universe under Palatini f(R) formalism. Starting by setting up the formalism needed, we have explored the field equations using Lemaitre–Tolman–Bondi geometry as an interior metric.
Yousaf, Z. +2 more
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