THE REPRESENTATION OF PROJECTIVE SPACES

Abstract

This chapter focuses on the representation of projective spaces. In flat affine geometry, an affine parameter is defined as a parameter for which the differential equations to the straight lines in Cartesian coordinates have the form, ▪. Similarly, in flat projective geometry, a projective parameter is most naturally defined as a parameter, for which the equations to the straight lines, in non-homogeneous projective coordinates have the form, ▪. The chapter also explains the equivalence problem and normal coordinates for normalized connections by proving the following theorems; any normal representation for a normalized projective connection is a selected representation, and two affinely equivalent normalized projective connections, referred to a selected representation, are equivalent under transformations of the form.