A geodesic mapping and its field of symmetric linear endomorphisms

It is well known that a geodesic mapping f:(M,g)→(M¯,g¯) is defined through the tensor field Af of type (1,1). In the present paper we give a geometric interpretation of eigenvalue function of the tensor field Af and consider a global aspect of the geometry of the geodesic mapping f:(M,g)→(M¯,g¯) with respect to the trace of Af.