On Kropina geodesic orbit spaces

The theory of Finsler spaces developed from the calculus of variations as well
as Riemannian geometry. To obtain Finsler spaces instead of Riemann spaces
we must replace the requirement that the space be locally Euclidean by the
requirement that it be locally Minkowskian. Since a Euclidean metric is also
Minkowskian, a Riemann space is also a Finsler space. In 1972, Matsumoto [20]
introduced the concept of (; )-metrics which are the generalization of Randers metric introduced by Randers The (; )-metrics form an important
class of Finsler metrics appearing iteratively in formulating Physics, Mechanics,
Seismology, Biology, Control Theory, etc..In this paper, we study Kropina spaces whose geodesics are the orbits of one-parameter subgroup of the group of isometries. Also, we study Kropina g.o. metrics on homogeneous spaces with two isotropy summands and we will investigate Kropina g.o. metrics
on compact homogeneous spaces with two isotropy summands. A complete characterization
of navigation data of non-Riemannian Kropina g.o. metrics is given.