Expression of the riemann tensor of a submanifold defined by a system of equations in euclidean space

In the paper the Riemann tensor of a submanifold of Euclidean space is expressed in terms of the derivatives of the defining functions and the components of the tangent vectors. The codimension 2 case, in particular the case of a two-dimensional surface inE ⁴, is treated in detail. As an example, the Gaussian curvature of the intersection of hyperquadrics with common axes is found. Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 3–9, July, 1999.