Riemann tensors

Riemann tensors

[′rē‚män ‚ten·sərz]
(mathematics)
Various types of tensors used in the study of curvature for a Riemann space.
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Concretely, the metric tensor, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the 3D domain are expressed by those on the 2D surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell.
Thus, the Riemann tensors on the middle surface S are defined by (cf.
Then, the covariant components of Riemann tensors on S are defined by
Thus, the Riemann tensors on [mathematical expression not reproducible] are defined by
Then, the covariant components of Riemann tensors on [??]([[bar.[OMEGA].sup.[epsilon]]) are defined by
Under the assumptions of Theorem 1, let [mathematical expression not reproducible] be the Riemann tensors on [mathematical expression not reproducible], respectively.
Einstein Ricci and Riemann tensors, and mind able to understand this