On some interpretation of linear frames in projective differential geometry

Abstract

The centroprojective group, i. e. the stabilizer G of a fixed point A in the group GP(n) of projective transformations of n-dimensional projective space Pn (n > 1) is considered in the paper. Two faithful representations of the linear quotient group of G are constructed: 1) the first one is on the linear frames, i. e. bases of tangent vector space to Pn at A; 2) the second one is on the equivalence classes of projective frames of Pn. It is shown that these representations are isomorphic. Geometrical interpretation for two frames to be equivalent is given.

Keywords

• projective space
• projective frame
• the projective trans­formations group
• quotient lie group
• lie group representation
• orbit spa­ce
• the desargues theorem