HARMONIC MAPS ON COTANGENT AND UNIT COTANGENT BUNDLES

Let (M, g) be an n-dimensional Riemannian manifold and (T * M,g(-)) be its cotangent bundle with a metricg that generalizes Sasaki and Cheeger-Gromoll metrics. In this paper, we investigate the harmonicity of the canonical projection pi : (T * M,g(-)) -> (M, g), the harmonicity of 1-forms regarded as maps sigma : (M, g) -> (T * M,g) and the harmonicity of the identity maps I-1 : (T * M,g(-)) -> (T * M, (S) g) and I-2 : (T * M, (S) g) -> (T * M,g(-)), where (S)g is the Sasaki metric. Moreover, we consider the same problems on the unit cotangent bundle T (1) *M .