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On Riemannian tangent bundles.

Adnan Al-Aqeel, Aurel Bejancu

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Abstract

Abstract. We study the geometry of manifolds whose tangent bundle is en-dowed with a Riemannian metric. The Levi-Civita connection, Schouten-Van Kampen connection and Vrănceanu 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.

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Abstract. We study the geometry of manifolds whose tangent bundle is en-dowed with a Riemannian metric. The Levi-Civita connection, Schouten-Van Kampen connection and Vrănceanu 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.

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Available abstract

Abstract. We study the geometry of manifolds whose tangent bundle is en-dowed with a Riemannian metric. The Levi-Civita connection, Schouten-Van Kampen connection and Vrănceanu 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.

Key concepts: Tangent bundle, Connection (principal bundle), Levi-Civita connection, Unit tangent bundle, Metric connection, Mathematics, Tangent, Fundamental theorem of Riemannian geometry

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