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.
New BDEs reveal singular surfaces from line congruences.
Study Blaschke's asymptotic lines on surfaces in 3D space.
The study explores Bertrand and Mannheim curves in 4D Euclidean space for framed curves.
Researchers find metric lines in SE(2) using Hamilton-Jacobi theory.
The Enneper surface and helix surfaces are unique in their geometric properties.
New methods create full discretized isothermic tori in Euclidean spaces.
The paper examines asymptotic lines of plane fields in 3D space.
Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.
The paper explores Bertrand and framed curves in 3D space.
The study analyzes Dirac operators twisted by specific bundles, revealing their geometric and regularity properties.
Consider a smooth map from a neighborhood of the origin in a real vector space to a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this …
We investigate some characteristic properties of specific Weingarten surfaces in the three-dimensional Euclidean space using the nets of the lines of curvature resp. the asymptotic lines on both central surfaces of them.
The purpose of this paper is, first, to give an algorithm that enables to obtain the lines of curvature on parametric hypersurfaces in Euclidean 4-space, and then, to obtain the curvatures of such lines by using the extended Darboux frame along the curve.
The Euclidean traveller explores various geometric spaces, seeing different places in each.
The classical Fundamental Theorem of Affine Geometry states that for , any bijection of -dimensional Euclidean space that maps lines to lines (as sets) is given by an affine map. We consider an analogous characterization of affine automorphisms for compact quotients, and establish it for tori: A bijection o…
Building on the work of and answering a question by Michael Harrison, we show that any contact structure on Euclidean 3-space induced by a line fibration is diffeomorphic to the standard contact structure.
In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E^{n}. Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line.
Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.
Defines and analyzes generalized normal ruled surfaces of curves in 3D space.
Study on minimal surfaces with closed curvature lines in 3D space.
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number of circles meeting in a given cyclic order given 6 disjoint smooth closed curves…
New surface class defined using osculating circles.
Isothermic parameterizations} are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of …
Stochastic gradient descent on manifolds improves low-rank approximation.
For any prescribed closed subset of a line segment in Euclidean 3-space, we construct a sequence of minimal disks that are properly embedded in an open solid cylinder around the segment and that have curvatures blowing up precisely at the points of the closed set.
We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in , as we illustrate with a number of explicit examples.
Smooth maps preserve distances on specific revolution surfaces.
Paper refines Talagrand inequality on Euclidean spaces.
Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with planar curvature lines in the Lorentz-Minkowski space has only recently been given. In this paper, we use an alternative method not only to re…
Following Riemann's idea, we prove the existence of a minimal disk in Euclidean space bounded by three lines in generic position and with three helicoidal ends of angles less than . In the case of general angles, we prove that there exist at most four such minimal disks, we give a sufficient condition of existence i…
This paper explores how rational numbers on the Stern-Brocot diagram map to lines when terms are extended.
Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular,…
The paper explores reflection principles for lightlike line segments on maximal surfaces.
The notion of max-plus convex subset of Euclidean space can be naturally extended to other linear spaces. The aim of this paper is to describe the topology of hyperspaces of max-plus convex subsets of Tychonov powers of the real line. We show that the corresponding spaces are AR's if and only if …
Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is sta…
In this note it is shown that the Maslov Index for pairs of Lagrangian Paths as introduced by Cappell, Lee and Miller appears by parallel transporting elements of (a certain complex line-subbundle of) the symplectic spinorbundle over Euclidean space, when pulled back to an (embedded) Lagrangian submanifold , along c…
We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball B_r^d \subset {\mathbb R}^d of radius r < 1/2 unless one of two conditions is met -- (1)The embedding manifold has dimension d >= 2m. (2) The embedding is not smoot…
Euclidean systems and real PK arrangements linked via geometry.
Characterizes ruled translating solitons in Minkowski 3-space.
It is well known that the space of oriented lines of Euclidean space has a natural symplectic structure. Moreover, given an immersed, oriented hypersurface S the set of oriented lines that cross S orthogonally is a Lagrangian submanifold. Conversely, if \bar{S} an n-dimensional family of oriented lines is Lagrangian, t…
A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notio…
Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such evolutoids. Besides, we used the theory of singularities to study the local behavior of r…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of such systems are observed when the plane is replaced by a regular surface in ${\mat…
We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to line or half-line, every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X. We construct an example of a complete path metr…
This study classifies metric lines in jet space.
Estimates modes and ridges in mixed Euclidean and directional spaces.
A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In this note we prove a global analogue of this result, as follows. Suppose that two …
The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and polyhedral metrics on the complex projective plane with singularities at a colle…