The geometry of tangent bundles and almost complex structures

Longwap, Silas and Massamba, Fortune (2017) The geometry of tangent bundles and almost complex structures. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (2). pp. 273-290. ISSN 0866-0174

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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 [7], 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.

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