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Towards Brin’s conjecture on frame flow ergodicity: new progress and perspectives
Mihajlo Cekić1; Thibault Lefeuvre2; Andrei Moroianu3; Uwe Semmelmann4
1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Université de Paris and Sorbonne Université, CNRS, IMJ-PRG, F-75006 Paris, France
3 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay, France
4 Institut für Geometrie und Topologie, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Mathematics Research Reports, Volume 3 (2022), pp. 21-34.

We report on some recent progress on the ergodicity of the frame flow of negatively-curved Riemannian manifolds. We explain the new ideas leading to ergodicity for nearly 0.25-pinched manifolds and give perspectives for future work.

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DOI: 10.5802/mrr.11
Classification: 37A05, 37A20, 37A25, 53C10, 53C22
Keywords: frame flow, geodesic flow, classical mechanics, ergodic theory, Pestov identity, Riemannian geometry, negative curvature, structure group, transitivity group, Parry’s free monoid, partially hyperbolic dynamical system
Mihajlo Cekić 1; Thibault Lefeuvre 2; Andrei Moroianu 3; Uwe Semmelmann 4

1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Université de Paris and Sorbonne Université, CNRS, IMJ-PRG, F-75006 Paris, France
3 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay, France
4 Institut für Geometrie und Topologie, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Mihajlo Cekić; Thibault Lefeuvre; Andrei Moroianu; Uwe Semmelmann. Towards Brin’s conjecture on frame flow ergodicity:  new progress and perspectives. Mathematics Research Reports, Volume 3 (2022), pp. 21-34. doi : 10.5802/mrr.11. https://mrr.centre-mersenne.org/articles/10.5802/mrr.11/

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