For the mean curvature vector field H and the Laplace operator ∆ of a submanifold in the Minkowski space, a submanifold satisfying the condition ∆H = f H + gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper...

In this paper, we investigate the surfaces generated by binormal motion of Bertrand curves, which is called Razzaboni surface, in Minkowski 3-space. We discussed the geometric properties of these surfaces in M according to the character of Bertrand geodesics. Then, we define the Razzaboni transformation for a given Razzaboni surface. In other words, we prove that there exists a dual of Razzabon...

Using techniques of integrable systems, we study a Weierstraß representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-space. The relationship between timelike minimal surfaces and bosonic Nambu-Goto ...

In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and geometric invariants of curves under the action of the Lorentz group. c ©2016 A...

Hasimoto [10] introduced the map from vortex filament solutions of Euler’s equations for incompressible fluids in the local induction approximation to solutions of the nonlinear Schrödinger equation and he showed vortex filament equation is equivalent nonlinear Schrödinger equation. After this discovering of Hasimoto, several authors [1, 5, 9, 12, 13, 14, 15, 17, 20, 21, 22, 23, 24] studied the...

In this paper we describe harmonic evolutes of surfaces in Minkowski 3-space. In particular, we study properties of harmonic evolutes of constant mean curvature surfaces and their relation to parallel surfaces. Furthermore, we study harmonic evolutes of surfaces of revolution. AMS subject classifications: 53A35, 53B30

1 Department of Mathematics, Faculty of Sciences, University of Çankiri Karatekin, 18100 Çankiri, Turkey 2 School of Mathematics & Statistical Sciences, Room PSA442, Arizona State University, Tempe, AZ 85287-1804, USA 3Department of Mathematics, Faculty of Sciences and Arts, University of Kirikkale, 71450 Kirikkale, Turkey 4Department of Mathematics and Informatics, Faculty of Science, Universi...