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Annals of Global Analysis and Geometry

, Volume 39, Issue 2, pp 187–213 | Cite as

Harmonic morphisms and Riemannian geometry of tangent bundles

  • Giovanni CalvarusoEmail author
  • Domenico Perrone
Article

Abstract

Let (TM, G) and \({(T_1 M,\tilde G)}\) respectively denote the tangent bundle and the unit tangent sphere bundle of a Riemannian manifold (M, g), equipped with arbitrary Riemannian g-natural metrics. After studying the geometry of the canonical projections π : (TM, G) → (M, g) and \({\pi_1:(T_1 M,\tilde G) \rightarrow (M,g)}\), we give necessary and sufficient conditions for π and π 1 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 \({\Phi:(TM-\{0\},G)\to (T_1 M,\tilde G)}\) with respect to Riemannian g-natural metrics \({G,\tilde G}\) of Kaluza–Klein type.

Keywords

Harmonic maps Harmonic morphisms Tangent and unit tangent sphere bundles Riemannian g-natural metrics 

Mathematics Subject Classification (2000)

58E20 53C43 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica “E. De Giorgi”Università del SalentoLecceItaly

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