On geodesics of Berger tangent sphere bundle of Hermitian locally symmetric manifold

We propose a special deformation of the Sasaki metric on tangent and unit tangent bundle of a Hermitian locally symmetric manifold. Geodesics of this deformed metric have different projections on a base manifold for tangent or unit tangent bundle cases in contrast to usual Sasaki metric. Nevertheless, the projections of geodesics of the unit tangent bundle still preserve the property to have all geodesic curvatures constant.

💡 Research Summary

The paper investigates a novel deformation of the classical Sasaki metric on the tangent bundle and the unit tangent sphere bundle of a Hermitian locally symmetric manifold. Starting from a Hermitian locally symmetric base ((M,J,g)), the authors introduce a “Berger‑type” modification of the Sasaki metric by adding a term proportional to the pull‑back of the fundamental 2‑form (\omega) of the Hermitian structure. Explicitly, the deformed metric is written as
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