Finsler spaces

In the first chapter, some fundamental definitions and results which will be used in other chapters have been given.In the second chapter, the definitions of metric space, normed space, minkowski norm and Riemannian metric and then propositions and examples which are connected with these definitions have been given.In the third chapter, Finslerian geometry, Finslerian structure, Legendre transformation have been defined and then the examples of Randers and Quartic metrics have been given.In the fourth chapter, geodesics have been taken up firstly in Riemann space and later in Finsler space. In Finsler manifold, the definitions such as a variation of a curve, geodesic coefficient and geodesic spray have been given.In the fifth chapter, in Finsler space, non-lineer connection, horizontal and vertical decompositions of \ and \ , sasaki metric and almost complex structure which are applications of the horizontal-vertical decomposition for \ have been introduced and some propositions which are connected with these definitions have been proved.In the sixth chapter, Connections and Covariant derivative have been taken up firstly in Riemann Space and later in Finsler space. In this chapter, the examples of Chern-Rund Connections, Hashiguchi Connection, Berwald and Cartan Connection have been given.In the seventh chapter, the definitions of curvatures in Riemann and Finsler space have been defined, some propositions have been given.Keywords: Finsler space , non-lineer connection , Legendre transformation , Randers metric.