The first part of the project aims to classify compact manifolds that admit locally conformally product (LCP) structures introduced by Matveev-Nikolayevsky and Kourganoff as a result of a conjecture by Belgun-Moroianu, which were recently studied by Flamencourt, Moroianu-Pilca and Andrada-del Barco-Moroianu. This theme has connections with locally conformally Kähler (LCK) geometry, with non-Kählerian complex geometry, especially through Oeljeklaus-Toma (OT) manifolds, and with the theory of solvmanifolds and of number fields.

The second part of the project aims to study the ergodicity properties of the frame flow considered by Gromov-Brin in the 80's on negatively curved compact manifolds. The methodology, recently introduced by Cekić-Lefeuvre-Moroianu-Semmelmann, is based on Pestov-Weitzenböck type formulas, twisted conformal Killing tensors and reductions of the structure groups of spheres.