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Infinitesimal bending of a subspace of a space with non-symmetric basic tensor. (English) Zbl 1088.53007

Let \(GR_N\) be a generalized Riemann space and \(GR_M\) be a subspace of \(GR_N\) given by the equations \(x^i = x^i(u^\alpha)\) in local coordinates. An infinitesimal deformation of \(GR_M\) is defined by equations of the form \(\bar{x}^i = x^i(u^\alpha) + \epsilon z^i(u^\alpha)\) with some vector field \(z^i(u^\alpha)\) along \(GR_M\). The authors investigate a special type of infinitesimal deformation called infinitesimal bending. The main results of the paper are derivation formulas of the infinitesimal bending vector field \(z^i(u^\alpha)\) and corresponding integrability conditions.

MSC:

53B20 Local Riemannian geometry
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References:

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