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On some properties of the Lie derivative in the space of linear elements. (Russian) Zbl 0673.53010
Let \(\Omega_{1}^ J\), \(\Omega_{2}^ K\) be linear differential- geometric objects of the first genus (quasitensors). In this paper the author proves the formula \[ {\mathcal D}(\Omega_{1}^ J\Omega_{2}^ K)=\Omega_{2}^ K\quad {\mathcal D}\Omega_{1}^ J+\Omega_{1}^ J\quad {\mathcal D}\Omega_{2}^ K \] for the Lie derivative of the object \(\Omega^{JK}=^{def}\Omega_{1}^ J\Omega_{2}^ K\). Other properties of the Lie derivative in the space of linear elements are also established.
Reviewer: F.C.Klepp
MSC:
53A55 Differential invariants (local theory), geometric objects
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