Generalized Bertrand Curves in Minkowski 3-Space

Biharmonic Curves in Minkowski 3-space

We give a differential geometric interpretation for the classification of biharmonic curves in semi-Euclidean 3-space due to Chen and Ishikawa (1991).

Generalized Timelike Mannheim Curves in Minkowski Space - Time E 41

On Pseudospherical Smarandache Curves in Minkowski 3-Space

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...

Biharmonic curves in Minkowski 3-space. Part II

This is a supplement to our previous research note [3]. In [3], we gave a characterization of biharmonic curves in Minkowski 3-space. More precisely, we pointed out that every biharmonic curves with nonnull principal normal in Minkowski 3-space is a helix, whose curvature κ and torsion τ satisfy κ2 = τ2. In the classification of biharmonic curves in Minkowski 3-space due to Chen and Ishikawa [1...

Caustics of de Sitter spacelike curves in Minkowski 3-space

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...