The geometry of generalised Cheeger-Gromoll metrics

Details The geometry of generalised Cheeger-Gromoll metrics The geometry of generalised Cheeger-Gromoll metrics

2007-03-02

arxiv.org/abs/math/0703059v2

Mathematics

Differential Geometry

Improved version with a larger class of parameters. A more detailed version is available on request

Scientific paper

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.

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