Abstract: We study the geometry of manifolds whose tangent bundle is endowed with a Riemannian metric. The Levi-Civita connection, Schouten-Van Kampen connection and Vranceanu connection are the main tools for this study. We obtain characterizations of special classes of vertical foliations and compare the sectional curvatures of the horizontal distribution with respect to the above connections.
Keywords: Riemannian tangent bundle, Levi-Civita, Schouten-Van Kampen and Vranceanu connections, vertical foliation, horizontal distribution, foliations with bundle-like metric, totally geodesic foliations, sectional curvature.
Classification (MSC2000): 53C12; 53B05
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