ON A SPECIAL CONCIRCULAR LIE-RECURRENCE IN A FINSLER SPACE

Abstract

The concept of Lie-recurrence in a Finsler space was introduced by the second author [8] of the present paper in 1982.The Lie-recurrence in a Riemannian space was studied by K. L. Duggal [3] in 1992 but he used the term curvature inheriting symmetry in place of Lie-recurrence. K. L. Duggal also applied the theory to the study of fluid space time. Since then both the terms (Lie-recurrence and curvature inheriting symmetry) are in use. The present authors [11], Shivalika Saxena and P. N. Pandey [12], [13], C. K. Mishra and Gautam Lodhi [1] studied a Lie-recurrence (curvature inheriting symmetry) in a Finsler space and discussed the possibilities for contra and concurrent vector fields to generate Lie-recurrence. The present paper deals with a Lie-recurrence generated by a special concircular vector field and such Lie-recurrence is termed as a special concircular Lie-recurrence. We obtain certain results related to a special concircular Lie-recurrence in a general Finsler space as well as in birecurrent and bisymmetric Finsler spaces. AMS Subject Classification: 53B40