The evolute of a conic in the pseudo-Euclidean plane is locus centers all its osculating circles. It’s curve order six and class four general case. In this paper we discuss compute evolutes different types conics. We will highlight those cases that have no analogy Euclidean plane.

A bounding region for spiral curve segments shaped by two circular arcs, parts of the osculating circles at the spiral’s endpoints, and two lines is introduced. This bounding region, denoted Spiral Fat Arc (SFA) is simple to construct and process, and shows a cubic approximation order to a given spiral curve. Given a general planar parametric curve, it can be split at curvature extrema (and inf...

We show how a type of multi-Frobenius nonclassicality curve defined over finite field Fq characteristic p reflects on the geometry its strict dual curve. In particular, in such cases we may describe all possible intersection multiplicities with linear system hyperplanes. Among other consequence, using result by Homma, are able to construct nonreflexive space curves that their tangent surfaces a...

In this paper, we focus on a developable surface tangent to timelike along curve in Minkowski 3-space, which is called the osculating of curve. The ruling parallel Darboux vector field. main goal paper classify singularities surface. To end, two new invariants curves are defined characterize these singularities. Meanwhile, also research singular properties surfaces near their lightlike points. ...

This study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized for n=1 (2n+s)-dimensional framed manifolds. Moreover, it studies some of proposed product’s basic properties. It also performs characterizations curvature Legendre curve on an S-manifold calculates curve. Furthermore, shows that curves are biharmonic curves. Next, t...

An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 or, equivalently, the derivatives of fj , fk are both parallel to fi. The Frenet frame (t,p,b) is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent t have attracted much in...

Abstract We study the intersection between a smooth algebraic surface with an umbilic point and plane parallel close to tangent at umbilic. The problem has its origin in of isophote (equal illumination) curves 2-dimensional image. In particular, we circles which have exceptional tangency this curve: ordinary one osculating another; three points; 4-point vertex. centres having two points trace o...

The aim of this paper is to define a new class surfaces in Euclidean space using the concept osculating circle. Given regular curve C, surface circles generated by C set all at points C. It proved that these contain one-parametric family planar lines curvature. A classification given canal surfaces, Weingarten with constant Gauss curvature and mean

Abstract We study the relation between type of a double point plane curve and curvilinear 0-dimensional subschemes at point. An Algorithm related to classical procedure for points via osculating curves is described proved. Eventually we look way create examples rational with given singularities $$A_s$$ A <mml:...