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 metric ~ g that generalizes Sasaki and Cheeger-Gromoll metrics. In this paper, we investigate the harmonicity of the canonical projection π : (T∗M; g~) ! (M; g); the harmonicity of 1-forms regarded as maps σ : (M; g) ! (T∗M; g~) and the harmonicity of the identity maps I1 : (T∗M; g~) ! (T∗M;S g) and I2 : (T∗M;S g) ! (T∗M; g~); where Sg is the Sasaki metric. Moreover, we consider same problems on the unit cotangent bundle T1∗M.