The geometry of tangent bundles and almost complex structures

Abstract: In this paper, we study the geometry of a tangent bundle of a Riemannian manifold endowed with a Sasaki metric. Using O'Neill tensors given in \cite{On}, we prove some characteristic theorems comparing the geometries of a smooth manifold and its tangent bundle. We also show that there exists an almost complex structure on a Riemannian manifold which is not holomorphic to the canonical almost complex structure of its tangent bundle.

Keywords: Tangent bundle; Sasakian metric; O'Neill tensor; Almost complex structure

Classification (MSC2000): 53C25; 53B20, 53B35

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