Related papers: Special Smarandache Curves in E1 3

In this paper we provide a characterization for a class of convex curves on the 3-sphere. More precisely, using a theorem that decomposes a locally convex curve on the 3-sphere as a pair of curves on the 2-sphere, one of which is locally…

A paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors of lines that would seem to require a discrete space. A class of continuous spaces is presented…

A new kind of partner curve called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some special curves such as slant helix, spherical helix, $C$-slant…

A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.

We investigate a family of correspondences associated to \'etale coverings of degree 3 of hyperelliptic curves. They lead to Prym-Tyurin varieties of exponent 3. We identify these varieties and derive some consequences.

In this study, after introducing algebraic properties of real quaternions some characterizations of quaternionic involute-evolute curves in Q are obtained. And some results and theorems for quaternionic w-curves are given. Lastly, we…

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.

The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…

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…

In this paper we present the definitions and some properties of several Samrandache Type Functions that are involved in many solved and unsolved problems and conjectures in number theory and recreational mathematics.

In this paper, we define some new associated curves as integral curves of a vector field generated by Frenet vectors of tangent indicatrix of a curve in Euclidean 3-space. We give some relationships between curvatures of these curves. By…

In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples:…

Morse foliations of codimension one on the sphere S^3 are studied and the existence of special components for these foliations is derived. As a corollary the instability of Morse foliations can be proven in almost all cases.

We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most…

In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean $3-$space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the…

We give some estimates of type sup*inf for equation of prescribed scalar curvature type in dimenion 3. As a consequence, we derive an uniqueness type result.

Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…

In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical…

The Cornu spirals on plane are the curves whose curvatures are linear. Generalized planar cornu spirals and Euler spirals in E^3, the curves whose curvatures are linear are defined in [1,5]. In this study, these curves are presented as the…

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We…