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. 
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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/

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[2] Eizenkhart L. P., Rimanova geometriya, IL, M., 1947

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