arXiv research

Study asymptotics of special curves on shrinking cylinders.

Compactifies curves in symplectizations with harmonic forms.

We investigate nicely embedded H--holomorphic maps into stable Hamiltonian three--manifolds. In particular we prove that such maps locally foliate and satisfy a no--first--intersection property. Using the compactness results of arXiv:0904.1603 we show that connected components of the space of such maps can be compactif…

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite energy foliations and the Weinstein conjecture, as well as in folded holomorphic …

The paper studies critical maps of a specific energy functional on pseudo-Hermitian manifolds.

Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We define folded holomorphic maps, i.e. pseudo-holomorphic maps that are discontinuou…

New methods to construct curve pairs and their applications.

New method to construct partner curves of non-lightlike curves.

The study explores Bertrand and Mannheim curves in 4D Euclidean space for framed curves.

The study examines Bertrand Legendre curves in the unit tangent bundle over Euclidean plane.

Method for generating new curves from plane curves on cylinders.

The paper characterizes curves in pseudo-Galilean 4-space.

The paper explores Bertrand and framed curves in 3D space.

Study introduces D-type curves on surface pencils and their properties.

The paper examines how closed curves on surfaces intersect and how this intersection determines the curves.

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given pr…

The study classifies singularities of spherical orthotomic curves.

Flow deforms locally convex curves to curves of constant k-order width.

Modified curve shortening flow constructs $λ$-Angenent curve.

Study on CR curves in 3-sphere, focusing on critical curves integration and existence.

The paper quantifies fractal curves using centroaffine curvatures.

Study rectifying curves in 3D multiplicative Euclidean space.

In classical curve theory, the geometry of a curve in three dimensions is essentially characterized by their invariants, curvature and torsion. When they are given, the problem of finding a corresponding curve is known as 'solving natural equations'. Explicit solutions are known only for a handful of curve classes, inc…

The paper characterizes pedal curves of quadratic curves.

Unified description of aesthetic curves through self-affinities.

Primitive curves in handlebodies form a connected complex.

Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.

Study isotopy of rational cuspidal curves in 4-manifolds.

Study uses isotropic projection to link plane and null curves in Minkowski space.

Defines new curves from tangent indicatrix of curves, linking them to helices and slant helices.

Study on triharmonic curves in f-Kenmotsu manifolds.

The paper generalizes rectifying and normal curves in Lorentzian n-space.

New findings on hyperbolicity of fine curve graphs and their subgraphs.

Study of $p$-biharmonic curves and their properties.

In this paper we study null Bertrand curves in $R_{1}^{4}$ under the assumption the curve has a Cartan frame. We show that if the derivative vectors of the null Cartan curve in $R_{1}^{4}$ is linearly independent, then this curve is not a Bertrand curve. Since then the already known notion of null Bertrand curves in $R…

Compact curve solution emerges from non-compact curve.

Homotopy types of curve and arc complexes are studied.

New curves generalize helix and rectifying curves.

We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura curves and of Teichmueller curves that reveals similarities and differences of the tw…

In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves and some special curves such as helix, slant helix or rectifying curves.

In this paper we consider the idea of Bertrand curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Bertrand D-curves and give the characterizations for these curves. We also find the relations between the geodesic curvatures, the normal curvatures and the geodesic…

The paper studies a curve flow preserving anisotropic length for convex curves, leading to a homothetic limit.

Characterizes covers using simple closed curves on surfaces.

Characterizes spherical and plane curves using RM frames.

Rectangular peg problem solved for many curves.

We study pairs of curves with Poncelet's porism properties and compute their vertex curves.

In this paper we consider the idea of Mannheim partner curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Mannheim partner D-curves and give the characterizations for these curves. We also find the relations between the geodesic curvatures, the normal curvatures …

Defines signed quasiregular curves and proves growth theorem.