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.