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

[摘要] 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 m ϕ , sinh m ϕ }, 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.

[关键词] Minkowski space;kinematic surfaces;homothetic motion;scalar curvature