The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available in certain applications and result in unstructured point cloud reconstructions.…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
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48 results for “Curved geometries”
Flow on curves in inversive geometry converges to loxodromics.
problem Gradient flow for curve length in inversive geometry.
method Invariant gradient flow for invariant length functional.
result Solutions exist for all time and converge to loxodromic curves.
Defines Lewy curves in para-CR geometry and characterizes their path geometries.
problem Characterizing path geometries defined by para-CR Lewy curves.
method Definition and characterization of para-CR Lewy curves in various dimensions.
result Lewy curves determine the para-CR structure up to sign in flat cases.
Study pseudo-hyperkähler geometry of curves in hyperkähler twistor spaces.
problem Understanding the geometry of rational curves in twistor spaces.
method Investigate pseudo-hyperkähler geometry of higher degree rational curves.
result Characterize the pseudo-hyperkähler structure of rational curves.
The paper explores quaternionic curves using differential geometry.
problem Understanding quaternionic curves.
method Differential geometry applied to quaternionic curves.
result Simpler formulations of quaternionic curves.
New aesthetic curves in equiaffine geometry include the quadratic and logarithmic spiral.
problem Designing aesthetic shapes in equiaffine geometry.
method Introducing a new symmetry (ESA) to characterize planar curves.
result The new class of curves includes the quadratic curve and logarithmic spiral.
Conformal Loxodromesmath.DG
Curved loxodromes on spheres are explained and their ODE derived.
problem Understanding curved analogues of compass-bearing curves on spheres.
method Explained curved loxodromes and derived the fifth order invariant ODE.
result Derived the fifth order invariant ODE for loxodromes.
A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curvesmath.DG
Study rectifying curves in 3D multiplicative Euclidean space.
problem Investigate rectifying curves in a non-Newtonian geometry setting.
method Apply multiplicative differential-geometric concepts to rectifying curves.
result Classify multiplicative rectifying curves using spherical curves.
Explains curves and surfaces in differential geometry.
problem Understanding smooth curves and surfaces in differential geometry.
method Problem-centered, elementary, visual approach focusing on essential techniques.
result Provides a solid foundation for further study in differential geometry.
Develops intrinsic curved cosets for Cartan geometries.
problem Defines curved cosets for arbitrary Cartan geometries.
method Defines intrinsic holonomy group and curved cosets.
result Curved cosets retain characteristics of homogeneous counterparts and behave well under automorphisms.
These notes introduce key techniques in differential geometry for curves and surfaces.
problem Understanding the basics of differential geometry for curve and surface analysis.
method Problem-centered, elementary, visual approach to teaching essential techniques.
result Provides a solid foundation for further study in differential geometry.
Survey on minimal rational curves and their geometric structures.
problem Germ-equivalence problem of minimal rational curves on uniruled projective manifolds.
method Analysis of isotrivial families of projective varieties and G-structures.
result Natural G-structure on Zariski-open subset of uniruled projective manifolds.
Study on Killing magnetic curves in Heisenberg group geometry.
problem Understanding Killing magnetic curves in Heisenberg group.
method Presentation of Heisenberg group geometry and geodesics, study of Killing magnetic curves with explicit formulas.
result Explicit formulas for Killing magnetic curves in Heisenberg group.
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.
Investigates the vertex curve of smooth surfaces in 3D space, connecting geometry and image analysis.
problem Understanding the geometry of smooth surfaces in 3D space.
method Analyzes the vertex curve, related to differential geometry and symmetry sets of isophote curves.
result Establishes connections between the vertex curve and other geometric curves like parabolic and flecnodal curves.
Unified description of aesthetic curves through self-affinities.
problem Characterizing log-aesthetic curves and their properties.
method Reformulating and proving self-affinities of planar curves, integrating equiaffine geometry.
result Unified characterization of constant curvature curves in similarity and equiaffine geometries.
The paper explores projective structures on curves and their applications in conformal geometry.
problem Finding qualitative information about solutions of Hill equations.
method Detailed description of projective structures and their isomorphism classes, correcting previous inaccuracies.
result The Yamabe problem for curves has no general solutions in a conformal/Möbius ambient space.
The paper proves an inequality and describes a curve flow in centro-affine geometry.
problem Proving the isoperimetric inequality in centro-affine plane geometry.
method Investigating a curve flow with centro-affine curvature, expressed as a nonlinear parabolic equation.
result Closed convex curves may converge to ellipses under the described flow.
We study the hyperkaehler geometry of a regular semisimple adjoint orbit of SL(k,C) via the algebraic geometry of the corresponding reducible spectral curve.
This paper studies CR geometry of transversal curves in the 3-sphere.
problem Investigating CR geometry of transversal curves in the 3-sphere.
method Using local CR invariants of the 3-sphere, four global invariants are considered: phase anomaly, CR spin, Maslov index, and CR self-linking number.
result Closed critical curves of the simplest CR invariant variational problem for generic transversal curves are studied.
We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski -space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the correspon…
All parabolic geometries, i.e. Cartan geometries with homogeneous model a real generalized flag manifold, admit highly interesting classes of distinguished curves. The geodesics of a projective class of connections on a manifold, conformal circles on conformal Riemannian manifolds, and Chern--Moser chains on CR--manifo…
Curved flats linked to pairs of Lie applicable surfaces.
problem Understanding curved flats in Lie sphere geometry.
method One-to-one correspondence with pairs of Demoulin families of Lie applicable surfaces via Darboux transformation.
result Curved flats correspond to specific Lie applicable surface pairs.
Study isotropic curves on complex quadric with geometric relations.
problem Characterize isotropic curves on the complex quadric.
method Analyze geometric properties and relations of isotropic curves.
result Discovers relations between isotropic curves and surfaces in spaceforms.
In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the complex of curves and the geometry of Teichmueller space.
The paper studies self-Bäcklund curves in centroaffine geometry using elliptic functions.
problem Understanding self-Bäcklund curves in centroaffine geometry.
method Description of general properties and detailed analysis using elliptic functions.
result Provides a detailed description of self-Bäcklund centroaffine curves in terms of elliptic functions.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
The paper shows that energy futures yield curves have an affine geometry.
problem Estimating dynamic behavior of yield curves from data while avoiding arbitrage.
method Finite dimensional models for yield curves, diffusion coefficients, and compatibility conditions.
result The compatibility of yield curves with diffusion coefficients forces an affine geometry.
The paper explores fully affine maximal curves and their properties.
problem Whether the hyperbola is the fully affine maximal curve in R^2.
method Utilizing evolution equations for curves, the second variational formula for fully affine extremal curves in R^2 was obtained.
result The fully affine maximal curves in R^2 are much more abundant and include explicit curves y=x^α (α is a constant and α∉{0,1,1/2,2}).
We study the conformal geometry of timelike curves in the (1+2)-Einstein universe, the conformal compactification of Minkowski 3-space defined as the quotient of the null cone of by the action by positive scalar multiplications. The purpose is to describe local and global conformal invariants of time…
The paper examines the geometry of a curve's centre symmetry set.
problem Global geometrical properties of a curve's centre symmetry set.
method Study of the envelope of affine chords.
result Number of singularities and asymptotes of the centre symmetry set.
Study connects flow dynamics to 3D geometry via surface intersections.
problem Relating flow dynamics to geometric properties of 3-manifolds.
method Relates pseudo-Anosov flow dynamics to hyperbolic geometry via curve graphs.
result Established a link between flow invariants and geometric features of 3-manifolds.
New insights into algebraic geometry of a conjecture, leading to origami curves.
problem Algebraic and geometric perspectives on the Putman-Wieland conjecture.
method Algebraic and geometric constructions of origami curves.
result Origami curves with high-dimensional isotrivial isogeny factors.
Study on curves around a Whitney umbrella focusing on geodesic and normal curvatures.
problem Analyzing geometric properties of curves around a specific surface.
method Examined geodesic and normal curvatures, ruled surfaces, and normal developable surfaces.
result Obtained functions representing geometry on a Whitney umbrella.
We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.
In this paper, we establish equiform differential geometry of space and timelike curves in 4-dimensional Minkowski space. We obtain some conditions for these curves. Also, general helices with respect to their equiform curvatures are characterized.
Study of curves in dual space with constant curvature and torsion.
problem Classifying curves in dual space with specific geometric properties.
method Defined curvature and torsion for curves in dual space, classified curves with constant properties, and proved existence theorems.
result Established fundamental theorem of existence for dual curves with prescribed curvature and torsion.
Sub-Riemannian geometry connects bike paths to mathematical curves.
problem Understanding bike paths and their mathematical properties.
method Relating sub-Riemannian geometry to bicycle motion and curve shapes.
result Geodesics in sub-Riemannian geometry correspond to specific bike paths.
Unique Teichmüller curve found in complex geometry.
problem Classifying Teichmüller curves in complex geometry.
method Complete classification of algebraically primitive Teichmüller curves.
result Veech 14-gon generates unique algebraically primitive Teichmüller curve.
Refined algebraic domains with finite sets in the boundaries respecting differential geometrymath.AG
Research on refined algebraic domains respecting differential geometry.
problem Understanding shapes and regions of real algebraic curves.
method Investigates points in two curves, singular points, inflection points, and points of double tangent lines, considering differential geometry.
result Proves fundamental properties and investigates examples of refined algebraic domains.
Study of rational curves in complex manifolds with specific normal bundles.
problem Characterizing rational curves in complex manifolds with given normal bundles.
method Analyzing differential and projective geometric properties of rational curves and their tangents.
result Classification of rational curves into Goursat and Cartan types based on their geometric properties.
Study curves of constant breadth in a specific 3D manifold.
problem Differential geometry of curves in Walker 3-manifolds.
method Investigate curves of constant breadth using Darboux frame.
result Properties of curves of constant breadth in Walker 3-manifolds.
The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection. Generalizations to parametrized curves, to higher-dimensional submanifolds and t…
Contact Geometry of Curvesmath.DG
Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group . The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the -equivalence problem via …
Study Kähler geometry on vector bundles over elliptic curves.
problem Characterize Kähler metrics on vector bundle total spaces.
method Analyzing function theory and Kähler geometry on vector bundles of degree zero.
result Biholomorphic total spaces correspond to isomorphic vector bundles.
Abstract: Study of surface transitions and IDE inflections via contact geometry.
problem Understanding transitions on surfaces and implicit differential equations.
method Contact geometry and Legendrian properties of projections.
result List of unavoidable local phenomena on surfaces and IDE solutions.
Novel multisymplectic framework for pseudo-Fueter curves in Hamiltonian field theory.
problem Generalizing Floer theory to multisymplectic geometry.
method Introducing pseudo-Fueter curves in a compatible almost hyperkähler structure.
result Gradient lines of multisymplectic action functional are pseudo-Fueter curves.
Solves index problem for curved BGG sequences in parabolic geometry.
problem Index theory of curved Bernstein-Gelfand-Gelfand sequences.
method Utilizes K-homology and noncommutative geometry.
result Solves the index problem for BGG-sequences on flat parabolic geometry.