Resumen de Integral geometry of the action of ST(3) on the space E3

Ana Berenice Guerrero Gutiérrez

• ABSTRACT. Some aspects of the integral geometry of the action on E3 of the group ST(3) of upper triangular 3x3-matrices of determinant one are studied Measurability for sets of linear surfaces is considered and it is shown that invariant measures do exist for sets of points or planes but not for sets of lines. Measurability for sets of couples point-line and point-plane is also discussed, and the existence of invariant measures is established in both cases. Explicit geometric formulae are given for the measures whenever they exist