An Expression for the Riemann Tensor of a Submanifold Given by a System of Equations in a Riemannian Space

We derive an expression for the Riemann tensor of a submanifold given implicitly by a system of independent equations in a Riemannian space. In particular, we prove a formula for the internal curvature of a two-surface in a three-dimensional Riemannian space. Some applications of the formula are given.