Some relationships between the geometry of the tangent bundle and the geometry of the Riemannian base manifold

DOI10.3836/TJM/1342701340zbMath1247.53034arXiv0912.5036OpenAlexW2017131745WikidataQ115219760 ScholiaQ115219760MaRDI QIDQ447797

Guillermo Henry, Guillermo G. R. Keilhauer

Publication date: 29 August 2012

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.5036

zbMATH Keywords

Riemannian manifoldstangent bundlenatural tensor fields

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Differential invariants (local theory), geometric objects (53A55) Methods of local Riemannian geometry (53B21)

Cites Work

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• On the geometry of the tangent bundle with the Cheeger-Gromoll metric
• Riemannian metrics on tangent bundles
• Tensor fields of type \((0,2)\) on the tangent bundle of a Riemannian manifold
• Curvatures of tangent bundles with Cheeger-Gromoll metric
• On some hereditary properties of Riemannian \(g\)-natural metrics on tangent bundles of Riemannian manifolds
• The fundamental equations of a submersion
• A formalism for the study of Natural Tensors Fields of type (0,2) on Manifolds and Fibrations

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