arXiv research

Each ruling of a Legendrian link can be naturally treated as a surface. For knots, the ruling is 2-graded if and only if the surface is orientable. For 2-graded rulings of homogeneous (in particular, alternating) knots, we prove that the genus of this surface is at most the genus of the knot. While this is not true in …

Study path geometries with constant torsion and cone structures.

It is proved that if a Paley-Wiener family of eigenfunctions of the Laplace operator in $\mathbb R^3$ vanishes on a real analytically ruled two-dimensional surface $S \subset \mathbb R^3$ then $S$ is a union of cones, each of which is contained in a translate of the zero set of a nonzero harmonic homogeneous polynomial…

Study of associative submanifolds in Berger space SO(5)/SO(3).

In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the differential equations characterizing slant ruled surfaces and if the reference ruled su…

In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is developable then the striction curve is a general helix or a slant helix accordi…

Study ruled surfaces with finite multiplicity, focusing on their curves and singularities.

In this study, we introduce Darboux slant ruled surfaces in the Euclidean 3-space which is defined by the property that the Darboux vector of orthonormel frame of ruled surface makes a constant angle with a fixed, non-zero direction. We obtain the characterizations of Darboux slant ruled surfaces regarding the conical …

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…

Study of ants' movement rules on a 6D space, revealing distribution structures and singular trajectories.

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 …

We compute all the simply connected homogeneous and infinitesimally homogeneous surfaces admitting one or more invariant affine connections. We find exactly six non equivalent simply connected homogeneous surfaces admitting more than one invariant connections and four classes of simply connected homogeneous surfaces ad…

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…

Paper proves every homogeneous Landsberg surface is either Riemannian or locally Minkowskian.

Study embeds ruled surfaces into symplectic manifolds, finds Stein fillability results.

New type of ruled surfaces studied with properties and examples.

In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski 3-space. Firstly, we define the Mannheim offsets of a timelike ruled surface by considering the Lorentzian casual character of the offset surface. We obtain that the M…

We classify ruled minimal surfaces in $\Bbb R^3$ with density $e^z.$ It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in $\Bbb R^3$ with density $e^z.$ It is also proved that all translation minimal surfaces are ruled.

The Lamarle Formula, given by Kruppa in \cite{Kr}, is known as a relationship between the Gaussian curvature and the distribution parameter of a ruled surface in the surface theory. The ruled surfaces were investigated in 3 different classes with respect to the character of base curves and rulings, \cite{Tu1},\cite{Tu2…

In this paper, we define dual geodesic trihedron(dual Darboux frame) of a spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled surfaces in dual Lorentzian space by considering the E. Study Mapping. We represent spacelike ruled surfaces by dual Lorentzian unit spherical curves and define Mannheim …

Study classifies ruled surfaces critical to Dirichlet energy.

Characterizes quasiconformally homogeneous ladder surfaces.

Is any positive knot the closure of a positive braid? No. But if we consider positivity in terms of the generators of the braid group due to Birman, Ko and Lee, then the answer is yes. In this paper we prove that the same occurs when considering homogeneity. In the way we prove that the plumbing of two surfaces is a BK…

In this paper, we consider non developable ruled surface with spacelike ruling, timelike ruling, respectively. We give the relations between the structure functions with the curvature and torsion of the striction line of the timelike and spacelike non developable ruled surfaces. Also, we have calculated the gaussian an…

Defines new ruled surfaces using alternative frames and analyzes their geometric properties.

We study locally homogeneous rigid geometric structures on surfaces. We show that a locally homogeneous projective connection on a compact surface is flat. We also show that a locally homogeneous unimodular affine connection on a two dimensional torus is complete and, up to a finite cover, homogeneous. Let $\nabla$ be …

In this paper, we introduce the dual geodesic trihedron (dual Darboux frame) of a timelike ruled surface. By the aid of the E. Study Mapping, we consider timelike ruled surfaces as dual hyperbolic spherical curves and define the Mannheim offsets of timelike ruled surfaces by means of dual Darboux frame. We obtain the r…

Study on risk contributions of portfolios using lambda quantile risk measures.

This study examines geometric properties and offsets of slant timelike-ruled surfaces.

Classifies special homogeneous surfaces with unique properties.

Paper classifies ruled surfaces in Lorentz-Minkowski space for a specific flow.

The paper classifies ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia.

Defines and analyzes generalized normal ruled surfaces of curves in 3D space.

Study on Kähler metrics on ruled surfaces, proving existence and non-existence.

Three types of Einstein metrics are disqualified as potential local maxima.

In this paper, we obtain the characterizations of Mannheim offsets of the timelike ruled surface with spacelike rulings in dual Lorentzian space. We give the relations between terms of their integral invariants and also we give the new characterization of the Mannheim offsets of developable timelike ruled surface. More…

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…

Study infinite symplectic forms on ruled surfaces.

Study of timelike surfaces with time-minimizing rulings in Newtonian and relativistic spacetimes.

Study classifies ruled surfaces from mean curvature flow solutions.

In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we obtain developable conditions for transversal surfaces of a timelike ruled surface.

The study characterizes constant curvature manifolds using ruled surfaces.

Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations of these ruled surfaces. Some special ruled surfaces such as normal surface, bino…

In this paper, using the classifications of timelike and spacelike ruled surfaces, we define and study the Mannheim offsets of spacelike ruled surfaces in Minkowski 3-space. We give the conditions for spacelike offset surfaces to be developable.

We study ruled surfaces in R3 which are obtained from dual spher- ical indicatrix curves of dual Frenet vector fields. We find the Gaussian and mean curvatures of the ruled surfaces and give some results of being Wein- garten surface.

Study ruled surfaces in 3D Riemannian manifolds, determining curvature and striction curves.

Characterizes ruled translating solitons in Minkowski 3-space.

The paper classifies ruled surfaces in a specific space that move in a special way.