Projective differential geometry of correspondences between two spaces. III

Correspondences between projective planes

We characterize integral homology classes of the product of two projective planes which are representable by a subvariety.

Prehomogenous spaces and projective geometry

Notes on Projective Differential Geometry

Projective differential geometry was initiated in the 1920s, especially by Élie Cartan and Tracey Thomas. Nowadays, the subject is not so well-known. These notes aim to remedy this deficit and present several reasons why this should be done at this time. The deeper underlying reason is that projective differential geometry provides the most basic application of what has come to be known as the ...

Differential Geometry of Submanifolds of Projective Space

These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of [16, 20, 29, 18, 19, 10, 31] are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new v...

Universal Hyperbolic Geometry III: First Steps in Projective Triangle Geometry

We initiate a triangle geometry in the projective metrical setting, based on the purely algebraic approach of universal geometry, and yielding in particular a new form of hyperbolic triangle geometry. There are three main strands: the Orthocenter, Incenter and Circumcenter hierarchies, with the last two dual. Formulas using ortholinear coordinates are a main objective. Prominent are five partic...