Isometric Extensions of Anosov Flows via Microlocal Analysis

The aim of this note is to revisit the classical framework developed by Brin and Pesin (Izv Akad Nauk SSSR Ser Mat 38:170-212, 1974), Brin (Mat Zametki 18(3):453-465, 1975, Funkcional Anal i Prilozen 9(1):9-19, 1975) and others to study ergodicity and mixing properties of isometric extensions of volume-preserving Anosov flows, using the microlocal framework developed in the theory of Pollicott-Ruelle resonances. The approach of the present note is reinvested in a crucial way in the companion paper (Cekic et al. in On the ergodicity of the frame flowon even-dimensional manifolds, 2021) in order to show ergodicity of the frame flow on negatively-curved Riemannian manifolds under nearly 1/4-pinched curvature assumption (resp. nearly 1/2-pinched) in dimension 4 and 4l + 2, l > 0 (resp. dimension 4l, l > 0).