Geodesic
An Expression for the Riemann Tensor of a Submanifold Given by a System of Equations in a Riemannian Space
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 643-648

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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. 
@article{MZM_2002_72_5_a0,
     author = {Yu. A. Aminov},
     title = {An {Expression} for the {Riemann} {Tensor} of a {Submanifold} {Given} by a {System} of {Equations} in a {Riemannian} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--648},
     publisher = {mathdoc},
     volume = {72},
     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a0/}
}
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Yu. A. Aminov. An Expression for the Riemann Tensor of a Submanifold Given by a System of Equations in a Riemannian Space. Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 643-648. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a0/