Lie-derivative of a linear connexion and various kinds of motions in a Kaehlerian recurrent space of first order (Q2869579)

The authors prove that in a linearly connected space \(L_n\) an infinitesimal transformation is an affine motion iff covariant and Lie derivations commute. After this, different motions are defined in a Kählerian recurrent space \(K_n\) of order \(1\), and it is proved that: {\parindent=6mm \begin{itemize}\item[1.] an infinitesimal transformation is a conformal motion iff \(\mathcal L g_{ij}=\Phi g_{ij}\); \item[2.] any motion is an affine motion; \item[3.] for a motion the Lie derivative of the curvature tensor \(K\) vanishes: \(\mathcal LK=0\); \item[4.] if \(K_n\) and \(^*K_n\) are in geodesic correspondence, and \(K_n\) admits a group of motion, then also \(^*K_n\) does so.NEWLINENEWLINE\end{itemize}}