On projective \(N\)-curvature inheritance (Q452803)

Curvature inheritance is an infinitesimal transformation with respect to which the Lie derivative of the curvature tensor is proportional with itself. Thus a curvature inheritance is a Lie recurrence. The authors prove that an infinitesimal transformation in a Finsler space is a Lie recurrence if and only if the normal projective curvature tensor \(N\) is Lie recurrent: \(\mathcal{L}N=\Phi N\), where \(\Phi\) is a scalar function independent of the directional argument.