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.
Uncountably many contractible 3-manifolds with double 3-space property and those without are identified.
Topology of non-orientable spaces without boundary is studied.
Defines Vassiliev complexity measures for open and closed curves in 3D space.
A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. In this paper we show that if a generic immersion of a planar g…
We analyze transverse doubled knots in the standard contact 3-space by using spanned clasp disks. As applications, we will estimate their self-linking number and furthermore we will show that in many cases, transverse twist knots with the maximal self-linking number are unique up to transverse isotopy.
Synthetic construction of Hopf fibration in 4D space.
Study affine curvature lines on surfaces in 3D space.
Links with isotopic preimages in are isotopic in .
Classifies generalized Seifert fiber spaces and their branched covers.
Classifies surfaces with special curvature properties.
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist loop in the special orthogonal group of rotations. We study a particularly simple, …
An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) iso…
Study on focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space.
We prove several topological properties of linear Weingarten surfaces of Bryant type, as wave fronts in hyperbolic 3-space. For example, we show the orientability of such surfaces, and also co-orientability when they are not flat. Moreover, we show an explicit formula of the non-holomorphic hyperbolic Gauss map via ano…
Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.
Study the geometry of lightlike loci on mixed type surfaces in Lorentz-Minkowski 3-space.
Introduces hyperbolic generalized framed surfaces and their properties.
We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also describe discrete focal …
Rotation minimizing vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed …
Paper tackles Santaló's convex surface problem in hyperbolic 3-space.
Integrable flows on null curves in anti-de Sitter 3-space studied.
New invariants measure entanglement of open curves in 3D space.
In this study, we define a family of ruled surfaces in the Euclidean 3-space E^3 and called similar ruled surfaces. We obtain some properties of these special surfaces and we show that developable ruled surfaces form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curv…
Study on tubes with specific Gauss map properties in 3D space.
Study on parabolic points and cylindrical surfaces in Euclidean 3-space.
We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral Kaehler structures. We prove that every rank one surface in these four manifolds i…
Non-compact convex sets in hyperbolic 3-space are rigid under isometries.
New knot models analyze local entanglement for robust curve analysis.
In this paper we discuss general properties of geodesic surfaces that are locally biLipschitz homogeneous. In particular, we prove that they are locally doubling and that there exists a special doubling measure analogous to the Haar measure for locally compact groups.
Defines the algebroid structure of double field theory.
In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…
Catenoids in de Sitter -space belong to a certain class of space-like constant mean curvature one surfaces. In a previous work, the authors classified such catenoids, and found that two different classes of countably many exceptional elliptic catenoids are not realized as closed subsets in . Here we s…
The hexabasic book is the cone of the 1-dimensional skeleton of the union of two tetrahedra glued along a common face. The universal 3-dimensional polyhedron UP is the product of a segment and the hexabasic book. We show that any 2-dimensional link in 4-space is isotopic to a surface in UP. The proof is based on a repr…
Until now, the only known maximal surfaces in Minkowski 3-space of finite topology with compact singular set and without branch points were either genus zero or genus one, or came from a correspondence with minimal surfaces in Euclidean 3-space given by the third and fourth authors in a previous paper. In this paper, w…
Delaunay tori minimize Willmore energy under isoperimetric constraints.
Combinatorial proof of grid homology properties.
We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H. Wente.
This study examines geometric properties and offsets of slant timelike-ruled surfaces.
Study simplifies homotopy groups of 6D manifolds.
In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3 form a family of similar ruled surfaces if and only if the striction curves of …
Study wave front singularities and their geometric properties.
Uniform doubling property proven for specific Lie groups.
The study characterizes loxodromes on specific rotational surfaces in 3D space.
Study on Whitehead doubles and their sliceness properties.
Characterizes a specific type of Courant algebroid with a Calabi-Yau structure.
Localization reveals geometric and analytic properties of the Witten genus.
Study on focal surfaces and evolutes of framed curves in hyperbolic 3-space using Legendrian duality.
In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representatio…