Actions of some mapping classes on the closed Riemann surfaces of genus two

The Teichmüller space of closed Riemann surfaces of genus two is considered as a subset of R 7 R^7 . We present some mapping classes acting on the model of the Teichüller space and investigate its action especially on the extremal surfaces with respect to a certain metric. As a result we estimate the distance between two orbits of distinct extremal surfaces from above.