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

TL;DR

This paper introduces a special deformation of the Sasaki metric on tangent bundles of Hermitian symmetric manifolds, revealing new geodesic behaviors and curvature properties distinct from the classical metric.

Contribution

It proposes a novel deformation of the Sasaki metric and analyzes the resulting geodesic properties on tangent and unit tangent bundles of Hermitian symmetric manifolds.

Findings

Deformed metric alters geodesic projections on the base manifold.

Geodesics in the deformed metric have different properties compared to the classical Sasaki metric.

Projections of geodesics in the unit tangent bundle maintain constant geodesic curvatures.

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.