The geometry of generalised Cheeger-Gromoll metrics

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JournalTokyo Journal of Mathematics
DatePublished - Dec 2009
Issue number2
Volume32
Number of pages26
Pages (from-to)287-312
Original languageEnglish

Abstract

We study the geometry of the tangent bundle equipped with a two-parameter family of Riemannian metrics. After deriving the expression of the Levi-Civita connection, we compute the Riemann curvature tensor and the sectional, Ricci and scalar curvatures. Specializing to the case of space forms, we characterise the metrics giving positive sectional curvature and show that one can always find parameters ensuring positive scalar curvature on the tangent space. Under some curvature conditions, this extends to general base manifolds.

    Research areas

  • Tangent bundle; , Cheeger-Gromoll metrics; , Positive scalar curvature;

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