Partially hyperbolic geodesic flow via conformal deformation

Abstract

This paper presents a new construction of non-Anosov partially hyperbolic geodesic flows. Our construction is closely related to the construction presented in [10] , the novelty is the use of conformal deformations to produce the examples. Some of the necessary conditions appear more naturally and are easier to check. Moreover, we can enumerate the conditions required to produce partially hyperbolic geodesic flow examples. We show how to produce examples with metrics that are non-positively curved, and with a finer analysis we can prove ergodicity for the Liouville measure and uniqueness of the measure of maximal entropy. These examples lie on the boundary of Anosov metrics, allowing us also to produce metrics with partially hyperbolic geodesic flows and conjugate points.