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In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of aRiemannian manifold $M$ which generalizes Sasaki metric and Cheeger Gromollmetric and a compatible almost complex structure which together with the metricconfers to $T(M)$ a structure of locally conformal almost K\"ahlerian manifold.This is the natural generalization of the well known almost K\"ahlerianstructure on $T(M)$. We found conditions under which $T(M)$ is almostK\"ahlerian, locally conformal K\"ahlerian or K\"ahlerian or when $T(M)$ hasconstant sectional curvature or constant scalar curvature. Then we willrestrict to the unit tangent bundle and we find an isometry with the tangentsphere bundle (not necessary unitary) endowed with the restriction of theSasaki metric from $T(M)$. Moreover, we found that this map preserves also thenatural almost contact structures obtained from the almost Hermitian ambientstructures on the unit tangent bundle and the tangent sphere bundle,respectively.Comment: 20 pages, LaTeX2e 4.1

Some Aspects on the Geometry of the Tangent Bundles and Tangent Sphere Bundles of a Riemannian Manifold