turkmath.org

In this talk first, we will define and give basic results about real projective structures on smooth manifolds. Then we will discuss such structures on two and three manifolds. Next we will mention the 2015 result by D. Cooper and W. Goldman that the smooth manifold ${\mathbb RP}^3\sharp {\mathbb RP}^3$does not admit any real projective structure (the first known example in dimension three), and we will generalize this result to all higher dimensions. If time permits, we will mention different type of examples of smooth manifolds with no real projective structure.