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.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
The study extends inscription problems to non-Euclidean geometries.
Geometric structures on surfaces relate to 2-plane distributions in 5D.
The study explores conformal planes with finite areas.
Study on isoperimetric problem in Randers planes achieving maximum area.
Only vertical planes are asymptotic to other planes in 3D space.
The study quantifies geodesic divergence on Riemannian planes with bounded geometry.
We prove that the Hilbert geometry of a convex domain in the plane is Gromov hyperbolic, if, and only if, the bottom of its spectrum is not zero
A new systolic inequality with a remainder for the real projective plane.
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…
In this work, the Z-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algeb…
Study hyperbolic geometry to find Fibonacci numbers.
The paper evaluates integrals of planes and their relation to convex set angles.
For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…
We study the integral expression of a knot invariant obtained as the second coefficient in the perturbative expansion of Witten's Chern-Simons path integral associated with a knot. One of the integrals involved turns out to be a generalization of the classical Crofton integral on convex plane curves and it is related w…
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
Proof of Graustein's theorem in different geometries.
Hopf algebra structure on the differential algebra of the extended -plane is defined. An algebra of forms which is obtained from the generators of the extended -plane is introduced and its Hopf algebra structure is given.
The paper extends curve deformation methods in Minkowski plane.
Plane Delaunay triangulations are rigid under Luo's discrete conformal change.
The "dancing metric" is a pseudo-riemannian metric of signature on the space of non-incident point-line pairs in the real projective plane . The null-curves of are given by the "dancing condition": the point is moving towards a point on the line, about which the li…
Classifies geodesic-preserving bijections in Thurston geometries.
We present a differential calculus on the extension of the quantum plane obtained considering that the (bosonic) generator is invertible and furthermore working polynomials in instead of polynomials in . We call quantum Lie algebra to this extension and we obtain its Hopf algebra structure and its dual H…
Crochet models of a hyperbolic plane is a popular educational tool as they help to visualize complicated objets in hyperbolic geometry. We present another way how to make crochet models when we view them as a part of a triangulated hyperbolic plane. We also provide a model of a cylinder in a hyperbolic space. This appr…
We present a complete set of criteria for determining A-types of plane-to-plane map-germs of corank one with A-codimension <7, which provides a new insight into the A-classification theory from the viewpoint of recognition problem. As an application to generic differential geometry, we discuss about projections of smoo…
Research explores Lorentzian distances on a specific geometric plane.
In this paper, by the method of moving planes, we prove the symmetry result which says that classical solutions of Monge-Ampere system in the whole plane are symmetric about some point. Our system under consideration comes from the differential geometry problem.
Following a recent paper by Baryshnikov and Zharnitskii, we consider outer billiards in the plane possessing invariant curves consisting of periodic orbits. We prove the existence and abundance of such tables using tools from sub-Riemannian geometry. We also prove that the set of 3-periodic outer billiard orbits has ze…
Study metrics on half plane with specific curvature properties.
Results on -dimensional topological planes are scattered in the literature. It is the aim of the present paper to give a survey of these geometries, in particular of information obtained after the appearance of the treatise Compact Projective Planes or not included in this book. For some theorems new proofs are give…
By a real alphabeta-geometry we mean a four-dimensional manifold M equipped with a neutral metric h such that (M,h) admits both an integrable distribution of alpha-planes and an integrable distribution of beta-planes. We obtain a local characterization of the metric when at least one of the distributions is parallel (i…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of…
The study finds bounds on metrics with constant curvature in the plane.
In this paper we consider the isoptic curves on the 2-dimensional geometries of constant curvature $\bE^2,~\bH^2,~\cE^2$. The topic is widely investigated in the Euclidean plane $\bE^2$ see for example \cite{CMM91} and \cite{Wi} and the references given there, but in the hyperbolic and elliptic plane there are few resu…
One-harmonic maps from a curved surface to hyperbolic plane have specific interior properties.
We study the geometry of the cuspidal edge in derived from its contact with planes and lines (referred to as flat geometry). The contact of with planes is measured by the singularities of the height functions on . We classify submersions on a model of by diffeomorphisms and recover the cont…
The paper proves an inequality and describes a curve flow in centro-affine geometry.
It is shown that coassociative cones in R^7 that are r-oriented and ruled by 2-planes are equivalent to CR-holomorphic curves in the oriented Grassmanian of 2-planes in R^7. The geometry of these CR-holomorphic curves is studied and related to holomorphic curves in S^6. This leads to an equivalence between associative …
Mathematical treatment of plane waves, proving their inextendibility and completeness.
Study flat connections with logarithmic singularities on complex plane curves.
New isoperimetric inequalities in the plane with radial weights identified.
New metrics derived from geodesics simplify semi-Riemannian geometry.
We express invariants of Finsler manifolds in a geometrical way by means of using moving planes and their associated Jacobi curves, which are curves in a fixed homogeneous Grassmann manifold. Some applications are given.
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally oriented. There are many natural classes of examples: links of singularities; links at…
In this paper results from the differential geometry of curves are extended from normed planes to gauge planes which are obtained by neglecting the symmetry axiom. Based on the gauge analogue of the notion of Birkhoff orthogonality from Banach space theory, we study all curvature types of curves in gauge planes, thus g…
Proof of Thurston's earthquake theorem using Anti-de Sitter geometry.
The axiom of θ-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed θ, 0< θ< π/2, then it is a real space form.