The geometry of generalised Cheeger-Gromoll metrics

Michele Benyounes; Eric Loubeau; Chris Wood

doi:10.3836/tjm/1264170234

The geometry of generalised Cheeger-Gromoll metrics

Michele Benyounes, Eric Loubeau, Chris Wood

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	287-312
Number of pages	26
Journal	Tokyo Journal of Mathematics
Volume	32
Issue number	2
DOIs	https://doi.org/10.3836/tjm/1264170234
Publication status	Published - Dec 2009

Keywords

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

Access to Document

10.3836/tjm/1264170234

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.tjm/1264170234

Cite this

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title = "The geometry of generalised Cheeger-Gromoll metrics",

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.",

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AU - Wood, Chris

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KW - Tangent bundle;

KW - Cheeger-Gromoll metrics;

KW - Positive scalar curvature;

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DO - 10.3836/tjm/1264170234

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