  In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a
Riemannian manifold $M$ which generalizes Sasaki metric and Cheeger Gromoll
metric and a compatible almost complex structure which together with the metric
confers to $T(M)$ a structure of locally conformal almost K\"ahlerian manifold.
This is the natural generalization of the well known almost K\"ahlerian
structure on $T(M)$. We found conditions under which $T(M)$ is almost
K\"ahlerian, locally conformal K\"ahlerian or K\"ahlerian or when $T(M)$ has
constant sectional curvature or constant scalar curvature. Then we will
restrict to the unit tangent bundle and we find an isometry with the tangent
sphere bundle (not necessary unitary) endowed with the restriction of the
Sasaki metric from $T(M)$. Moreover, we found that this map preserves also the
natural almost contact structures obtained from the almost Hermitian ambient
structures on the unit tangent bundle and the tangent sphere bundle,
respectively.
