TWO-DIMENSIONAL SURFACES IN EUCLIDEAN 5-SPACE WITH CONSTANT SCALAR CURVATURE

In this paper, we analyzed the problem of studying locally the scalar curvature
of the three dimensional surfaces foliated by an equiform motion of catenary curve in Euclidian five spaceΕ . We express the scalar curvature
of the corresponding two-dimensional surfaces as the quotient of functions cosh  , sinh , and we derive the necessary and sufficient conditions for the coefficients to vanish identically. Finally an example is given to show threedimensional surfaces with constant scalar curvature.