Let $(M, g)$ be a compact Riemannian manifold and $T_1M$ its unit tangent sphere bundle. We equip $T_1M$ with an arbitrary Riemannian g-natural metric $˜G$ , and investigate the harmonicity of a unit vector field V of $M$, thought as a map from $(M, g)$ to $(T_1M, ˜G )$. We then apply this study to characterize unit Killing vector fields and to investigate harmonicity properties of the Reeb vector field of a contact metric manifold.
Harmonicity of unit vector fields with respect to Riemannian g-natural metrics
CALVARUSO, Giovanni;PERRONE, Domenico;
2009-01-01
Abstract
Let $(M, g)$ be a compact Riemannian manifold and $T_1M$ its unit tangent sphere bundle. We equip $T_1M$ with an arbitrary Riemannian g-natural metric $˜G$ , and investigate the harmonicity of a unit vector field V of $M$, thought as a map from $(M, g)$ to $(T_1M, ˜G )$. We then apply this study to characterize unit Killing vector fields and to investigate harmonicity properties of the Reeb vector field of a contact metric manifold.File in questo prodotto:
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