Affine motion in RNP-Finsler space (Q796837)

An NP-recurrent Finsler space is a Finsler space whose normal projective curvature tensor \(N^ i_{jkh}\) is recurrent. The authors call RNP- Finsler space an NP-recurrent Finsler space endowed with an infinitesimal transformation defined by a vector v and satisfying \(L_ v\lambda_ s=0\), where \(\lambda_ s\) is the recurrence covector and \(L_ v\) means the Lie derivative with respect to v. Various properties of RNP-Finsler spaces are proved. For example, the condition under which \(L_ vN^ i_{jkh}\equiv 0\) and a necessary and sufficient condition for the existence of an affine motion are established.