GEODESIC LINES IN $D$ RECURRENT FINSLER SPACES

Irena Comi\'c

Abstract: A $D$ recurrent Finsler space is defined as a Finsler space in which the absolute differential of the metric tensor is recurrent. For some special cases of the parameter and the vector of recurrency some interesting special cases are obtained. An example is the non-recurrent Finsler space with Cartain connection coefficients. After introducing the so called $Y$ connection [5], it is examined in which special case of a $D$ recurrent Finsler space the introduced $Y$ connection will give a recurrent Riemannian space. Finally different kinds of definition of a geodesic line are given. The relation between them and the projective change of the metric function are examined. It is prooved that in a $D$ recurrent Finsler space the geodesic line does not depend on the connection coefficients, but only on the metric function of the space.

Classification (MSC2000): 53C60

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