Let (TM, G) and (T1M, ˜G ) respectively denote the tangent bundle and the unit tangent sphere bundle of a Riemannian manifold (M, g), equipped with arbitraryRiemannian g-natural metrics. After studying the geometry of the canonical projections π : (TM, G) → (M, g) and π1 : (T1M, ˜G) → (M, g), we give necessary and sufficient conditions for π and π1 to be harmonic morphisms. Some relevant classes of Riemannian g-natural metrics will be characterized in terms of harmonicity properties of the canonical projections. Moreover, we study the harmonicity of the canonical projection : (TM −{0}, G) → (T1M, ˜G ) with respect to Riemannian g-natural metrics G, ˜G of Kaluza–Klein type.
Harmonic morphisms and Riemannian geometry of tangent bundles
CALVARUSO, Giovanni;PERRONE, Domenico
2011-01-01
Abstract
Let (TM, G) and (T1M, ˜G ) respectively denote the tangent bundle and the unit tangent sphere bundle of a Riemannian manifold (M, g), equipped with arbitraryRiemannian g-natural metrics. After studying the geometry of the canonical projections π : (TM, G) → (M, g) and π1 : (T1M, ˜G) → (M, g), we give necessary and sufficient conditions for π and π1 to be harmonic morphisms. Some relevant classes of Riemannian g-natural metrics will be characterized in terms of harmonicity properties of the canonical projections. Moreover, we study the harmonicity of the canonical projection : (TM −{0}, G) → (T1M, ˜G ) with respect to Riemannian g-natural metrics G, ˜G of Kaluza–Klein type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
