Harmonic morphisms and Riemannian geometry of tangent bundles |
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Authors: | Giovanni Calvaruso Domenico Perrone |
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Institution: | 1.Dipartimento di Matematica “E. De Giorgi”,Università del Salento,Lecce,Italy |
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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. |
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