In this paper, we study translation surfaces generated by spherical indicatrices of timelike curves in Minkowski 3-space and find necessary sufficient conditions for the to be flat or minimal. Further, obtain generating geodesic, asymptotic line curvature. Finally such axis when they are constant angle surfaces.

This paper describes an approach we suggest to monitor pavements by using an active optical device. Basically, the amount of light received by such sensors depends on superficial conditions, for which studying some specific traits of scattering indicatrices can bring substantial information. With this objective in sight, the major physical processes originating in the observed back-scattering a...

This paper concentrates on the requirements of being an integral curve for geodesic spray natural lift curves spherical indicatrices timelike-spacelike involute-evolute pair in Lorentz 3-space. In addition, obtained results were supported by one example.

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce ne...

BACKGROUND This study introduces two novel outcomes that could be used to identify people with knee osteoarthritis from healthy controls. These outcomes examine the lengths of paths on a sphere derived from knee angle and knee position during gait. METHODS Participants with moderate knee osteoarthritis (n=47) and no knee pathology (n=51) walked overground. The time-varying orientation matrice...

The well-known invariants of conics are computed for classes of Finsler and Lagrange spaces. For the Finsler case, some (α, β)-metrics namely Randers, Kropina and ”Riemann”-type metrics provides conics as indicatrices and a Randers-Funk metric on the unit disk is treated as example. The relations between algebraic and differential invariants of (α, β)-metrics are pointed out as a method to use ...

In this paper, we investigate the spherical images of null curves and helixes in Minkowski 3-space. We provide indicatrices 3-space with their causal characteristics. also show conditions to be a curve lying on pseudo-sphere addition, give properties satisfying generalized helices