In this paper, we analyze involutes of pseudo-null curves in Lorentz–Minkowski 3-space.
Pseudo-null curves are spacelike curves with null principal normals, and their involutes can …

Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an
alternative to the Frenet frame. They are used in CAGD because they can be defined even …

We discuss how the shape of a special Cosserat rod can be represented as a path in the
special Euclidean algebra. By shape we mean all those geometric features that are invariant …

In this work, we are interested in the differential geometry of curves in the simply isotropic
and pseudo-isotropic 3-spaces, which are examples of Cayley-Klein geometries whose …

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant
characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical …

Abstract We consider curves γ:[0, 1]→ R 3 endowed with an adapted orthonormal frame r:[0,
1]→ SO (3). We wish to deform such framed curves (γ, r) while preserving two contraints: a …

In this paper, we analyze the intrinsic geometry of lightlike planes in the three-dimensional
Lorentz–Minkowski space M 3. We connect the theory of curves lying in lightlike planes in M …

We give necessary and sufficient conditions on the curvature and the torsion of a regular
curve of the space forms\({\mathbb {H}}^ 3\) and\({\mathbb {S}}^ 3\) to be contained in a …

The consideration of the so-called rotation minimizing frames allows for a simple and
elegant characterization of plane and spherical curves in Euclidean space via a linear …

In this paper, we introduce Bishop frame of a partially null curve α in Minkowski space-time
E41. We prove that such curve has three Bishop frames determined by the particular …