Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space

Abstract

In this paper we analyzed the problem of studying locally the scalar curvature S of the two dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space E17 $\text{E}^7_1$ . We express the scalar curvature S of the corresponding kinematic surfaces as the quotient of hyperbolic functions {cosh mϕ, sinh mϕ}, and we derive the necessary and sufficient conditions for the coefficients to vanishes identically. Finally, an example is given to show two dimensional kinematic surfaces with zero scalar curvature.

Keywords

• minkowski space
• kinematic surfaces
• homothetic motion
• scalar curvature
• 53a05
• 53a17
• 53b30