No Null-Helix Mannheim Curves in the Minkowski Space E13

ASSOCIATED CURVES OF THE SPACELIKE CURVE VIA THE BISHOP FRAME OF TYPE-2 IN E₁³

The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obta...

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...

k−type partially null and pseudo null slant helices in Minkowski 4-space

We introduce the notion of a k-type slant helix in Minkowski space E1. For partially null and pseudo null curves in E1, we express some characterizations in terms of their curvature and torsion functions. AMS subject classifications: 53C40, 53C50

Generalized Timelike Mannheim Curves in Minkowski Space - Time E 41

Time-like Involutes of a space-like helix in Minkowski space-time

In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...