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 connects hyperbolic spinors to non-null framed curves in Minkowski 3-space.
The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.
In this paper, the Cartan frames and the equi-affine curvatures are described with the help of the Frenet frames and the Frenet curvatures of a non-null and non-degenerate curve in a 3-dimensional pseudo-Riemannian manifold. The constancy of the Frenet curvatures of such a curve always implies the constancy of the equi…
In this study, non-null Frenet-Mannheim curves and non-null Weakened Mannheim curves are investigated in Minkowski 3-space. Some characterizations for this curves are obtained.
Study on evolutes and focal surfaces of pseudo-spherical framed immersions in anti-de Sitter space.
In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion. We determine all non-null self-similar curve…
The study examines null curves in specific geometric manifolds and their properties.
In this paper we study the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group. We prove that all of the non-geodesic non-null biharmonic curves in 3-dimensional hyperbolic Heisenberg group are helices. Moreover, we obtain explicit parametric equations for non-geodesic non-null biharmon…
This paper defines directional derivatives and solves Maxwell's equations in curved 3D space.
In an earlier paper, I defined a new winding number of regular closed curves on complete euclidean/hyperbolic surfaces and showed that this winding number, together with the free homotopy class, determines the regular homotopy class. In this paper, I give a Whitney-type formula for the winding number of non-null-homoto…
Research shows curves in Walker 3-manifolds can lie in flat cylinders.
In this paper, we study inextensible flows of non-null curves in E^n,1. We give necessary and sufficient conditions for inextensible flow of nonnull curves in E^n,1.
In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a non-null ruled surface to be a slant ruled surface in E_1^3. Moreover, we obtain some corollaries which give the relationships between a non-null slant…
In this paper, we investigate the tangent indicatrix of the curve C with constant curvature. Tangent indicatrix of the curve C is characterized with det(C^(3),C^(4),C^(5))=0 in Minkowski 3-space E13. Moreover, we study null slant helices using the determinant approach and give the following characterization: A curve C …
Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.
Study of generalized Bishop frames on curves in 4D space.
We show that the skein vector space of the 3-torus is finitely generated. We show that it is generated by 9 elements: the empty set, some simple closed curves representing the non null elements of the first homology group with coefficients in \Z_2, and a link consisting of two parallel copies of one of the previous non…
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
The study explores Bertrand and Mannheim curves in 4D Euclidean space for framed curves.
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in …
Study of generalized Bishop frames on time-like curves in 4D Lorentz space.
Study on focal surfaces and evolutes of framed curves in hyperbolic 3-space using Legendrian duality.
New method studies moving points on curves using rotating frames.
Defines non-parabolic curves in spatial hybrid space with applications.
The paper defines evolutes and involutes for framed curves and their properties.
Generalized Frenet frames for singular space curves
The paper explores Bertrand and framed curves in 3D space.
Study null surfaces of pseudo-spherical curves in anti-de Sitter space.
Bertrand framed surfaces defined in Euclidean 3-space with applications.
In this paper we study the general affine geometry of curves in affine space . For a regular plane curves we define two kinds of moving frames. The first is of minimal order in all moving frames.The second is the Frenet moving frame. We get the moving equations of these moving frames. And we prove that curvature a…
Discussing moving frames for curve and surface invariants.
For a regular curve on a spacelike surface in Lorentz-Minkowski -space, we have a moving frame along the curve which is called a Lorentzian Darboux frame. We introduce five special vector fields along the curve associated to the Lorentzian Darboux frame and investigate their singularities.
In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is also an eikonal Darboux helix for timelike and spacelike curves. Furthermore, we ob…
In this paper, we study spinor Bishop equations of curves in E^3. We research the spinor formulations of curves according to Bishop frames in E^3. Also, the relation between spinor formulations of Bishop frames and Frenet frame are expressed.
Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized functional on the space of framed curves of arbitrary parameterization, which model rods with axial stretch or cross-secti…
The Frenet frame is generally known an orthonormal vector frame for curves. But, it does not always meet the needs of curve characterizations. In this study, with the help of associated curves of any spatial curve we obtained a new orthonormal frame which has the property that the second vector makes a constant angle w…
Study curves of constant breadth in a specific 3D manifold.
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the first time in 4-dimensional Euclidean space. Then we obtain the conditio…
The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are considered, adapted frames and osculating frames, in terms of certain differential …
In this study, we determine some special Smarandache curves according to Darboux frame in E3. We give some characterizations and consequences of Smarandache curves.
In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.
Quaternionic curves with specific torsion properties don't exist.
Framework for isometric immersions of planar regions from framed curves.
We analyzed the problem of finding a surfaces family through an asymptotic curve with Cartan frame. We obtain the parametric representation for surfaces family whose members have the same as an asymptotic curve. By using the Cartan frame of the given null curve, we present the surface as a linear combination of this fr…
In this paper, we have first given easily the characterization of special curves with the help of the Rotation minimizing frame (RMF). Also, rectifying-type curves are generalized n-dimensional space .
In this paper, we study helices and the Bertrand curves. We obtain some of the classification results of these curves with respect to the modified orthogonal frame in Euclidean 3-spaces.
In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the equivalence of the non-linear Schrödinger equation and non-linear heat system to the…
In this study, we consider AW(k)-type curves according to the Bishop Frame in Euclidean space E^3. We give the relations between the Bishop curvatures k_1, k_2 of a curve in E^3.