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Abstract

The concept of a Lie recurrence was introduced by the first author [6]. It is an infinitesimal transformation with respect to which the Lie derivative of a curvature tensor is proportional to itself. Apart from other results related to a Lie recurrence, it was established that the Weyl projective curvature tensor is Lie recurrent with respect to a Lie recurrence but its converse is not necessarily true. However, an infinitesimal transformation with respect to which the Weyl projective curvature tensor and the Ricci tensor are Lie recurrent, is necessarily a Lie recurrence. Singh [12] studied an infinitesimal transformation with respect to which the Lie derivative of the curvature tensor is proportional to itself and called such transformation as curvature inheritance. Obviously, a curvature inheritance is nothing but a Lie recurrence. Singh [13] also considered a curvature inheritance which is a projective motion and called it a projective curvature inheritance. Gatoto and Singh [1,2] studied -curvature inheritance and projective -curvature inheritance. Pandey and Pandey [9] studied projective Lie recurrence. Mishra and Yadav [3] studied projective curvature inheritance in an NP-F n. In the present paper we have established that an infinitesimal transformation in a Finsler space is Lie recurrence if and only if the normal projective curvature tensor is Lie recurrent. A part from this result we have generalized almost all theorems of Mishra and Yadav [3].

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