Kinematic formulas for the real subspaces of complex space forms of dimension 2 and 3

Abstract

The prinicpal kinematic formulas for complex space forms of dimension 2 and 3 are deduced. Namely, for given two good subsets A and B of the complex space forms of dimension 2 or 3, the mean value of the Euler characteristic x(A?gB) over the group of motions is computed in terms of curvature measures of A and B.