According to the damage mechanics theorem, the flexibility tensor variation may externalize the macroscopic effect of rockmass damage.

The concept of additional flexibility tensor is introduced to indicate the influence of seepage pressure on the mechanic characteristics of rock mass.

To mathematically characterize the deformation of the middle surface of a shell,the metric tensor and curvature tensor ought to be investigated in detail.

On the basis of metric tensor of known crust surface,the formula of crustral deformation tensor,principal direction, linear strain, area strain, Gaussian and mean curture on crust surface calculated with GPS observation data are given.

Using von Mises yield criterion with anisotropic damage involved, the fourth-order symmetrical elasto-plastic-damage stiffness tensor is obtained.

According to the metric tensor of the four dimensional time space continual redgion, this paper further solve the Einstein s equation and offered the quantitave computation to the tiperihelion precession of the celestial body moving in orbit in centric symmetry gravitational field.

Using the Friedmann Space theory,We have discussed some problems on cosmology,Themain conclusions are: 1 metric tensor of the Friedmann space;2 energy-momentum tenosr of the Friedmann space;3 therelation of space cvolution to temperature;4 the theory formula of Red shift.