Search

The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski 3-space. Some characterizations according to the curvatures and torsions of the curves are given. Finally, some relations under the conditions for Mannheim curves and their partner curves to be generalized helices are presented. All the possible cases for the partner curves to be spacelike and timelike are considered in the whole of the article.

The Frenet frame is not suitable for describing the behavior of the curve in the Galilean space since it is not defined everywhere. In this study, an alternative frame, the so-called quasi-frame, is investigated in Galilean 4-space. Furthermore, the quasi-formulas in Galilean 4-space are deduced and quasi- curvatures are obtained in terms of the quasi-frame and its derivatives. Quasi- rectifying, quasi-normal, and quasi-osculating curves are studied in Galilean 4-space. We prove that there is no quasi-normal and accordingly normal curve in Galilean 4-space. [ABSTRACT FROM AUTHOR]

The aim of this research paper was to explore the various characteristics of the doubly warped product manifold, focusing particularly on aspects such as the Hessian, Riemannian curvature, Ricci curvature, and concircular curvature tensor components. By examining the necessary conditions that would classify the manifold as Riemann-flat, Ricci-flat, and concircularly-flat, the study aimed to expand our understanding of these concepts. To achieve this, the research incorporated the application of these findings to a generalized Robertson-Walker doubly warped product manifold scenario. This approach allowed us to identify and analyze the specific circumstances under which the manifold displayed concircular flatness. [ABSTRACT FROM AUTHOR]

In this article, we present the equiform parameter and define the equiform‐Bishop frame in Minkowski 3‐space E 1 3. Additionally, we investigate the equiform‐Bishop formulas of the equiform spacelike case in Minkowski 3‐space. Furthermore, some results of equiform spacelike normal curves according to the equiform‐Bishop frame in E 1 3 are considered. [ABSTRACT FROM AUTHOR]