Calculation Scalar Curvature of the Cycloid Surface in R⁵

In this work, we show a local study of a cyclic surface in R⁵ produced by equiform motions of a cycloid. We definepartially such surfaces with some conjecture on its curvature. In general, we shall consider the condition that scalar curvature is locally constant. We will conclude cases of scalar curvature of following equations accounts and will put theories to explain the results of research and example.