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

Alexander Yampolsky

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arXiv · 0706.3298

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

Alexander Yampolsky

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Abstract

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.

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Alexander Yampolsky. 2007-06-22. On geodesics of Berger tangent sphere bundle of Hermitian locally symmetric manifold. https://arxiv.org/abs/0706.3298

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