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 study explores Bertrand and Mannheim curves in 4D Euclidean space for framed curves.
In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the dimensional pseudo-Euclidean space of index two. Also we characte…
In [18], L. R. Pears proved that Bertrand curves in E-n(n > 3) are degenerate curves. This result restate in [16] by Matsuda and Yorozu. They proved that there is no special Bertrand curves in E-n(n > 3) and they define new kind of Bertrand curves called (1, 3)-type Bertrand curves in 4-dimensional Euclidean space. In …
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
In this paper, we introduce the quaternionic similar curves in 4-dimensional Euclidean space. We show that the families of quaternionic curves with vanishing curvatures form the families of quaternionic similar curves.
In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.
In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We characterize rectifying curves in the -dimensional Euclidean space in different ways…
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.
In [5], Matsuda and Yorozo obtained that Mannheim curves in 4-dimensional Euclidean space. In this study, we define quaternionic Mannheim curves and we give some characterizations of them in Euclidean 3-space and 4-space.
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…
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 study, we try to semi-real quaternionic curves in the semi-Euclidean space E_2^4. Firstly, we introduce algebraic properties of semi-real quaternions. And then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E_2^4. Lastly, we illustrate some examples…
The paper studies singularities on parallels of tangent developable surfaces of frontal curves.
New parametrizations for minimal timelike surfaces discovered.
Quasiregular curves are Hölder continuous and have higher integrability.
In this study we consider AW(k)-type curves according to parallel transport frame in Euclidean space E^4. We give the relations between the parallel transport curvatures of these kinds of curves.
In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.
In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its …
Defines and analyzes generalized normal ruled surfaces of curves in 3D space.
The paper explores Bertrand and framed curves in 3D space.
Study of generalized Bishop frames on time-like curves in 4D Lorentz space.
In this paper, we study the special curves and ruled surfaces on helix hypersurface whose tangent planes make a constant angle with a fixed direction in Euclidean n-space Besides, we observe some special ruled surfaces in and give requirement of being developable of the ruled surface. Also, we investigate the helix sur…
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
Study rectifying curves in 3D multiplicative Euclidean space.
The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and n_2 of the curve. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifyin…
In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.
Smooth curves with specific curvature can be closely approximated.
The study examines elastic curves with self-intersections and their properties.
New method classifies geodesics on cones.
The paper characterizes rectifying curves on smooth surfaces using isometries and Darboux frames.
A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some re…
We prove that for every analytic curve in the complex plane, Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in Euc…
New findings on hypersurfaces in Euclidean space that are both maximal and minimal.
A curve around a sphere must be at least 4π long.
A space curve in a Euclidean 3-space is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [Amer. Math. Monthly {\bf 110} (2003), no. 2, 147-152]. In this present article, we introduce and study the n…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a…
The paper defines evolutes and involutes for framed curves and their properties.
New formula for curvatures of curves in n-dimensional space.
Characterizes ruled translating solitons in Minkowski 3-space.
The paper tackles Kakeya and Nikodym sets on curved manifolds, reducing problems to Euclidean space.
The orthogonal trajectories of the first tangents of the curve are called the involutes of . The hyperspheres which have higher order contact with a curve are known osculating hyperspheres of . The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve in $n…
Bertrand framed surfaces defined in Euclidean 3-space with applications.
Classifies soap film surfaces with vertical potentials.
New, algebraic surfaces found in curved spaces.
Interpolates curves using maximal and minimal surfaces in different spaces.
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hami…
Using the idea of special Legendre curves, the authors obtained the explicit description of flat Lagrangian H-umbilical submanifolds in quaternion Euclidean spaces.
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…