Real projective structures on Riemann surfaces

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, as well as compact K¨ahler surfaces, focusing on the fundamental problem

Gunning, Analytic structures on the space of flat vector bundles over a compact Riemann surface, Several complex variables, II (Proc.. Lecture Notes in

If M is a compact Riemann surface of genus g ^ 2, in each free homotopy class of a homotopically non trivial closed curve there is a unique closed geodesic (this is due to the

i° Soit (S^) une exhaustion de la surface parabolique S, ^n(/), q) la fonction de Green de S^. Pour q et Çy fixes sur S, la famille des fonctions y^Çp ; ç. îo) est noi'male,

— We investigate the action of the automorphism group of a closed Riemann surface of genus at least two on its set of theta charac- teristics (or spin structures).. We give

To explain the second result let us denote by S(X) the set of line- bundles (up to isomorphism) which are square roots of the canonical line bundle of X. In fact it is clearly

— A toute surface de Biemann (3^ simplement connexe, représentable par un arbre topologique régulièrement ramifié, sans polygones infinis, on peut associer une surface de Riemann

Comme [9] peut être limite de rayons par valeurs supérieures ou inférieures, il se pourrait que certains arcs de A soient aussi des arcs y. La propriété ci-dessus montre donc que