Abstract
The covarient derivative of an arbitrary contravariant vector X^i in the sense of Berwald in a Finsler space F_n is given by (1.1) X_((j))^i = ∂ ̇_j X^i- (∂ ̇_j X^i ) G_j^k+ X^k G_kj^i , where G_jk^i (x ,x ̇ ) is the connection parameter introduced by Berwald and is defined by (1.2) G_jk^i = ∂ ̇_jk^2 〖 G〗^i , which is the positively homogeneous of degree zero in its directional arguments . The geodesic deviation has been given in the following form ( Rund [6] ) (1.3) (δ^2 Z^j)/(δu^2 ) + H_k^j (x,x ̇) Z^k = 0, where the vector Z^i is called the “variation vector” and the tensor H_k^j (x,x ̇) is called the “deviation tensor” defined by (1.4) H_k^j (x,x ̇) = K_ihk^j x ̇^i x ̇^h
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