Some harmonic problems for deformed Sasaki metrics on tangent bundles
Volume 53 / 2026
Applicationes Mathematicae 53 (2026), 61-82
MSC: Primary 53C20; Secondary 53C43, 58E20
DOI: 10.4064/am2555-4-2025
Published online: 3 October 2025
Abstract
We investigate some harmonic problems on the tangent bundle with a deformed Sasaki metric. Firstly, we study the harmonicity of a vector field with respect to this metric, and we construct some examples of harmonic vector fields. Secondly, we study the harmonicity of a vector field along a map between Riemannian manifolds, where the tangent bundle of the target manifold is equipped with a deformed Sasaki metric. Finally, we discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, where the tangent bundle of the first manifold is equipped with a deformed Sasaki metric.
