16 may 2019 -- 11:30
Aula Tricerri, DiMaI, Firenze
It is a classical result of Hirzebruch that the quaternion projective spaces do not admit almost complex structures. In my talk I want to show how to use the Atiyah Singer index theorem to obtain a very short alternative proof working for a much larger class of manifolds. In particular it is possible to decide which positive quaternion Kähler manifolds and which symmetric spaces of inner type admit almost complex structures. My talk is based on joint work with Paul Gauduchon and Andrei Moroianu.