Projective algebraic manifolds are an equivalent definition for projective varieties. Projective hyperplanes, are used in projective geometry. Points in the affine component of the projective plane have coordinates . Every intersection of projective subspaces is a projective subspace. It is the study of geometric properties that are invariant with respect to projective transformations. They later investigated W-curves, curves invariant under a group of projective transformations. In algebraic geometry, this construction allows for greater flexibility in the construction of projective bundles. Another topic that developed from axiomatic studies of projective geometry is finite geometry. A generalization of a non-degenerate conic in a projective plane is an oval. It is an instance of Galois geometry, a study of projective geometry using finite fields. It was realised that the theorems that do apply to projective geometry are simpler statements. Cayley constructed the Chow variety of all curves in projective 3-space. A Klein bottle is homeomorphic to the connected sum of two projective planes. Photogrammetry uses methods from many disciplines, including optics and projective geometry. This notion finds utility in projective geometry and complex analysis.