AFFINE MOTION IN RECURRENT AREAL SPACES OF SUBMETRIC CLASS

We consider affine motion in recurrent areal space of submetric class , denoted by A*}'""1. The necessary and sufficient conditions are obtained when affine motions admit contra -fields . Other special cases are also discussed. In a set of papers K. Takano ([1] ,[2]) has studied affine motion in non-Riemannian K* -spaces . Affine motions in recurrent Finsler was studied by R.S.Sinha [5] . T. Igarashi[4] has introduced the theory of Lie-derivative in an areal space of submetric class . The concept of deformed areal spaces and the homothetic transformations in areal space of submetric class was developed by O.P.Singh ([6],[7]) . Recently the present author [8] discussed the motion with contra field in a symmetric areal space of submetric class. In this paper the author wishes to study affine motion in recurrent areal space of submetric class.